%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET641+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:05 AM UTC 2025
% Result : Theorem 0.91s 1.09s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET641+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:32:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.91/1.09 % SZS status Theorem
% 0.91/1.09 % SZS output start Proof
% 0.91/1.09 tff(member_type, type, (
% 0.91/1.09 member: ( $i * $i ) > $o)).
% 0.91/1.09 tff(tptp_fun_B_10_type, type, (
% 0.91/1.09 tptp_fun_B_10: $i)).
% 0.91/1.09 tff(tptp_fun_D_3_type, type, (
% 0.91/1.09 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.91/1.09 tff(cross_product_type, type, (
% 0.91/1.09 cross_product: ( $i * $i ) > $i)).
% 0.91/1.09 tff(tptp_fun_D_12_type, type, (
% 0.91/1.09 tptp_fun_D_12: $i)).
% 0.91/1.09 tff(tptp_fun_C_11_type, type, (
% 0.91/1.09 tptp_fun_C_11: $i)).
% 0.91/1.09 tff(ilf_type_type, type, (
% 0.91/1.09 ilf_type: ( $i * $i ) > $o)).
% 0.91/1.09 tff(set_type_type, type, (
% 0.91/1.09 set_type: $i)).
% 0.91/1.09 tff(power_set_type, type, (
% 0.91/1.09 power_set: $i > $i)).
% 0.91/1.09 tff(subset_type, type, (
% 0.91/1.09 subset: ( $i * $i ) > $o)).
% 0.91/1.09 tff(relation_type_type, type, (
% 0.91/1.09 relation_type: ( $i * $i ) > $i)).
% 0.91/1.09 tff(member_type_type, type, (
% 0.91/1.09 member_type: $i > $i)).
% 0.91/1.09 tff(empty_type, type, (
% 0.91/1.09 empty: $i > $o)).
% 0.91/1.09 tff(subset_type_type, type, (
% 0.91/1.09 subset_type: $i > $i)).
% 0.91/1.09 tff(1,plain,
% 0.91/1.09 ((ilf_type(B!10, set_type) & (ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))) <=> (ilf_type(B!10, set_type) & ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(2,plain,
% 0.91/1.09 ((~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))) <=> (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12)))))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(3,plain,
% 0.91/1.09 ((ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12)))))) <=> (ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[2])).
% 0.91/1.09 tff(4,plain,
% 0.91/1.09 ((ilf_type(B!10, set_type) & (ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))) <=> (ilf_type(B!10, set_type) & (ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12)))))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[3])).
% 0.91/1.09 tff(5,plain,
% 0.91/1.09 ((ilf_type(B!10, set_type) & (ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))) <=> (ilf_type(B!10, set_type) & ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))),
% 0.91/1.09 inference(transitivity,[status(thm)],[4, 1])).
% 0.91/1.09 tff(6,plain,
% 0.91/1.09 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))) <=> (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D)))))))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(7,plain,
% 0.91/1.09 ((~![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))))))) <=> (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D)))))))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(8,axiom,(~![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_relset_1_3')).
% 0.91/1.09 tff(9,plain,
% 0.91/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.91/1.09 tff(10,plain,
% 0.91/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.91/1.09 tff(11,plain,
% 0.91/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.91/1.09 tff(12,plain,
% 0.91/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.91/1.09 tff(13,plain,
% 0.91/1.09 (ilf_type(B!10, set_type) & ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12)))))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.91/1.09 tff(14,plain,
% 0.91/1.09 (ilf_type(C!11, set_type)),
% 0.91/1.09 inference(and_elim,[status(thm)],[13])).
% 0.91/1.09 tff(15,plain,
% 0.91/1.09 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(16,plain,
% 0.91/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[15])).
% 0.91/1.09 tff(17,plain,
% 0.91/1.09 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(18,plain,
% 0.91/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[17])).
% 0.91/1.09 tff(19,plain,
% 0.91/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[18, 16])).
% 0.91/1.09 tff(20,plain,
% 0.91/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(21,plain,
% 0.91/1.09 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)) <=> ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), (![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)) <=> ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(22,plain,
% 0.91/1.10 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[21])).
% 0.91/1.10 tff(23,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4')).
% 0.91/1.10 tff(24,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.91/1.10 tff(25,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.91/1.10 tff(26,plain,(
% 0.91/1.10 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.10 inference(skolemize,[status(sab)],[25])).
% 0.91/1.10 tff(27,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.91/1.10 tff(28,plain,
% 0.91/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type)))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(29,plain,
% 0.91/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(30,plain,
% 0.91/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.91/1.10 tff(31,plain,
% 0.91/1.10 (![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[30, 27, 14])).
% 0.91/1.10 tff(32,plain,
% 0.91/1.10 (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))),
% 0.91/1.10 inference(and_elim,[status(thm)],[13])).
% 0.91/1.10 tff(33,plain,
% 0.91/1.10 (ilf_type(D!12, set_type)),
% 0.91/1.10 inference(or_elim,[status(thm)],[32])).
% 0.91/1.10 tff(34,plain,
% 0.91/1.10 (((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))) | ((~ilf_type(D!12, set_type)) | ilf_type(cross_product(C!11, D!12), set_type))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))) | (~ilf_type(D!12, set_type)) | ilf_type(cross_product(C!11, D!12), set_type))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(35,plain,
% 0.91/1.10 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))) | ((~ilf_type(D!12, set_type)) | ilf_type(cross_product(C!11, D!12), set_type))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(36,plain,
% 0.91/1.10 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))) | (~ilf_type(D!12, set_type)) | ilf_type(cross_product(C!11, D!12), set_type)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.91/1.10 tff(37,plain,
% 0.91/1.10 (ilf_type(cross_product(C!11, D!12), set_type)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[36, 33, 31])).
% 0.91/1.10 tff(38,plain,
% 0.91/1.10 (ilf_type(B!10, set_type)),
% 0.91/1.10 inference(and_elim,[status(thm)],[13])).
% 0.91/1.10 tff(39,plain,
% 0.91/1.10 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(40,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[39])).
% 0.91/1.10 tff(41,plain,
% 0.91/1.10 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(42,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[41])).
% 0.91/1.10 tff(43,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.10 inference(transitivity,[status(thm)],[42, 40])).
% 0.91/1.10 tff(44,plain,
% 0.91/1.10 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(45,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[44])).
% 0.91/1.10 tff(46,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(47,plain,
% 0.91/1.10 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))) <=> (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))), ((ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), rewrite((ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) <=> ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))), ((ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))))), (![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(48,plain,
% 0.91/1.10 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[47])).
% 0.91/1.10 tff(49,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10')).
% 0.91/1.10 tff(50,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.91/1.10 tff(51,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.91/1.10 tff(52,plain,(
% 0.91/1.10 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))),
% 0.91/1.10 inference(skolemize,[status(sab)],[51])).
% 0.91/1.10 tff(53,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.91/1.10 tff(54,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.91/1.10 tff(55,plain,
% 0.91/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C)))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C)))))))))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(56,plain,
% 0.91/1.10 (((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) <=> ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C)))))))))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(57,plain,
% 0.91/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[56])).
% 0.91/1.10 tff(58,plain,
% 0.91/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C)))))))))),
% 0.91/1.10 inference(transitivity,[status(thm)],[57, 55])).
% 0.91/1.10 tff(59,plain,
% 0.91/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(60,plain,
% 0.91/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.91/1.10 tff(61,plain,
% 0.91/1.10 (![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[60, 54, 38])).
% 0.91/1.10 tff(62,plain,
% 0.91/1.10 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(63,plain,
% 0.91/1.10 (((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(cross_product(C!11, D!12))) | (~((~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12))))))))) <=> ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(64,plain,
% 0.91/1.10 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(cross_product(C!11, D!12))) | (~((~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))))))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[63])).
% 0.91/1.10 tff(65,plain,
% 0.91/1.10 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(cross_product(C!11, D!12))) | (~((~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))))),
% 0.91/1.10 inference(transitivity,[status(thm)],[64, 62])).
% 0.91/1.10 tff(66,plain,
% 0.91/1.10 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(cross_product(C!11, D!12))) | (~((~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))))))))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(67,plain,
% 0.91/1.10 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))))))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.91/1.10 tff(68,plain,
% 0.91/1.10 (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[67, 61, 37])).
% 0.91/1.10 tff(69,plain,
% 0.91/1.10 (((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))))) | ((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(70,plain,
% 0.91/1.10 ((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.91/1.10 tff(71,plain,
% 0.91/1.10 (^[B: $i] : refl(((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type))))) <=> ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type))))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(72,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[71])).
% 0.91/1.10 tff(73,plain,
% 0.91/1.10 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type))))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(74,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[73])).
% 0.91/1.10 tff(75,plain,
% 0.91/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(76,plain,
% 0.91/1.10 (^[B: $i] : rewrite((ilf_type(B, set_type) => ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(77,plain,
% 0.91/1.11 (![B: $i] : (ilf_type(B, set_type) => ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[76])).
% 0.91/1.11 tff(78,axiom,(![B: $i] : (ilf_type(B, set_type) => ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11')).
% 0.91/1.11 tff(79,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.91/1.11 tff(80,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.91/1.11 tff(81,plain,(
% 0.91/1.11 ![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 0.91/1.11 inference(skolemize,[status(sab)],[80])).
% 0.91/1.11 tff(82,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.91/1.11 tff(83,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.91/1.11 tff(84,plain,
% 0.91/1.11 (((~![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(85,plain,
% 0.91/1.11 ((~![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)))))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(86,plain,
% 0.91/1.11 ((~![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.91/1.11 tff(87,plain,
% 0.91/1.11 (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[86, 83, 37])).
% 0.91/1.11 tff(88,plain,
% 0.91/1.11 ((empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type))) | (~empty(power_set(cross_product(C!11, D!12))))),
% 0.91/1.11 inference(tautology,[status(thm)],[])).
% 0.91/1.11 tff(89,plain,
% 0.91/1.11 (~empty(power_set(cross_product(C!11, D!12)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.91/1.11 tff(90,plain,
% 0.91/1.11 ((empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type))) | ilf_type(power_set(cross_product(C!11, D!12)), set_type)),
% 0.91/1.11 inference(tautology,[status(thm)],[])).
% 0.91/1.11 tff(91,plain,
% 0.91/1.11 (ilf_type(power_set(cross_product(C!11, D!12)), set_type)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.91/1.11 tff(92,plain,
% 0.91/1.11 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(93,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[92])).
% 0.91/1.11 tff(94,plain,
% 0.91/1.11 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(95,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[94])).
% 0.91/1.11 tff(96,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 0.91/1.11 inference(transitivity,[status(thm)],[95, 93])).
% 0.91/1.11 tff(97,plain,
% 0.91/1.11 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(98,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[97])).
% 0.91/1.11 tff(99,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(100,plain,
% 0.91/1.11 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C))) <=> ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))), (![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C))) <=> ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))), ((ilf_type(B, set_type) => ![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))), ((ilf_type(B, set_type) => ![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(101,plain,
% 0.91/1.11 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[100])).
% 0.91/1.11 tff(102,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12')).
% 0.91/1.11 tff(103,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.91/1.11 tff(104,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.91/1.11 tff(105,plain,(
% 0.91/1.11 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 0.91/1.11 inference(skolemize,[status(sab)],[104])).
% 0.91/1.11 tff(106,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.91/1.11 tff(107,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.91/1.11 tff(108,plain,
% 0.91/1.11 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(109,plain,
% 0.91/1.11 (((~ilf_type(B!10, set_type)) | ![C: $i] : ((ilf_type(B!10, member_type(C)) <=> member(B!10, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ((~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(110,plain,
% 0.91/1.11 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((ilf_type(B!10, member_type(C)) <=> member(B!10, C)) | empty(C) | (~ilf_type(C, set_type))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[109])).
% 0.91/1.11 tff(111,plain,
% 0.91/1.11 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((ilf_type(B!10, member_type(C)) <=> member(B!10, C)) | empty(C) | (~ilf_type(C, set_type))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C))))),
% 0.91/1.11 inference(transitivity,[status(thm)],[110, 108])).
% 0.91/1.11 tff(112,plain,
% 0.91/1.11 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((ilf_type(B!10, member_type(C)) <=> member(B!10, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(113,plain,
% 0.91/1.11 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.91/1.11 tff(114,plain,
% 0.91/1.11 (![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[113, 107, 38])).
% 0.91/1.11 tff(115,plain,
% 0.91/1.11 (((~![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))) | (empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12)))))) <=> ((~![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))) | empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12)))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(116,plain,
% 0.91/1.11 ((~![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))) | (empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12)))))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(117,plain,
% 0.91/1.11 ((~![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))) | empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.91/1.11 tff(118,plain,
% 0.91/1.11 (empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12))))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.91/1.11 tff(119,plain,
% 0.91/1.11 (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[118, 91, 89])).
% 0.91/1.11 tff(120,plain,
% 0.91/1.11 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(121,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[120])).
% 0.91/1.11 tff(122,plain,
% 0.91/1.11 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(123,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[122])).
% 0.91/1.11 tff(124,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(transitivity,[status(thm)],[123, 121])).
% 0.91/1.11 tff(125,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(126,plain,
% 0.91/1.11 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))) <=> ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))), (![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(127,plain,
% 0.91/1.11 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[126])).
% 0.91/1.11 tff(128,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7')).
% 0.91/1.11 tff(129,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.91/1.11 tff(130,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.91/1.11 tff(131,plain,(
% 0.91/1.11 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(skolemize,[status(sab)],[130])).
% 0.91/1.11 tff(132,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.91/1.11 tff(133,plain,
% 0.91/1.11 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12)))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12)))))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(134,plain,
% 0.91/1.11 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12)))))))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(135,plain,
% 0.91/1.11 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.91/1.11 tff(136,plain,
% 0.91/1.11 (![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[135, 132, 37])).
% 0.91/1.11 tff(137,plain,
% 0.91/1.11 (((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))) | ((~ilf_type(B!10, set_type)) | (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))) | (~ilf_type(B!10, set_type)) | (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(138,plain,
% 0.91/1.11 ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))) | ((~ilf_type(B!10, set_type)) | (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(139,plain,
% 0.91/1.11 ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))) | (~ilf_type(B!10, set_type)) | (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.91/1.11 tff(140,plain,
% 0.91/1.11 (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[139, 38, 136])).
% 0.91/1.11 tff(141,plain,
% 0.91/1.11 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(142,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[141])).
% 0.91/1.11 tff(143,plain,
% 0.91/1.11 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(144,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[143])).
% 0.91/1.11 tff(145,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 0.91/1.11 inference(transitivity,[status(thm)],[144, 142])).
% 0.91/1.11 tff(146,plain,
% 0.91/1.11 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(147,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[146])).
% 0.91/1.11 tff(148,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(149,plain,
% 0.91/1.11 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C))))) <=> (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))), ((ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))))) <=> (ilf_type(C, set_type) => (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))), rewrite((ilf_type(C, set_type) => (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))) <=> ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))), ((ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))))) <=> ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))), (![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C))))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(150,plain,
% 0.91/1.11 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[149])).
% 0.91/1.11 tff(151,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p1')).
% 0.91/1.11 tff(152,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.91/1.11 tff(153,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.91/1.11 tff(154,plain,(
% 0.91/1.11 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 0.91/1.11 inference(skolemize,[status(sab)],[153])).
% 0.91/1.11 tff(155,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.91/1.11 tff(156,plain,
% 0.91/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[155, 145])).
% 0.91/1.11 tff(157,plain,
% 0.91/1.11 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C))))))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(158,plain,
% 0.91/1.11 (((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))))))) <=> ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C))))))))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(159,plain,
% 0.91/1.12 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C)))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))))))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[158])).
% 0.91/1.12 tff(160,plain,
% 0.91/1.12 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C)))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C))))))))),
% 0.91/1.12 inference(transitivity,[status(thm)],[159, 157])).
% 0.91/1.12 tff(161,plain,
% 0.91/1.12 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C)))))))))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(162,plain,
% 0.91/1.12 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))))))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.91/1.12 tff(163,plain,
% 0.91/1.12 (![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))))))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[162, 156, 14])).
% 0.91/1.12 tff(164,plain,
% 0.91/1.12 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))))))) | ((~ilf_type(D!12, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))))))) | (~ilf_type(D!12, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))))))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(165,plain,
% 0.91/1.12 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))))))) | ((~ilf_type(D!12, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))))))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(166,plain,
% 0.91/1.12 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))))))) | (~ilf_type(D!12, set_type)) | (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12))))))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.91/1.12 tff(167,plain,
% 0.91/1.12 (~((~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[166, 33, 163])).
% 0.91/1.12 tff(168,plain,
% 0.91/1.12 (((~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))) | (~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12))))) | ![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))),
% 0.91/1.12 inference(tautology,[status(thm)],[])).
% 0.91/1.12 tff(169,plain,
% 0.91/1.12 (![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.91/1.12 tff(170,plain,
% 0.91/1.12 (~ilf_type(B!10, relation_type(C!11, D!12))),
% 0.91/1.12 inference(or_elim,[status(thm)],[32])).
% 0.91/1.12 tff(171,plain,
% 0.91/1.12 (((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | ((~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))) | ilf_type(B!10, relation_type(C!11, D!12)))) <=> ((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))) | ilf_type(B!10, relation_type(C!11, D!12)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(172,plain,
% 0.91/1.12 ((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | ((~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))) | ilf_type(B!10, relation_type(C!11, D!12)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(173,plain,
% 0.91/1.12 ((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))) | ilf_type(B!10, relation_type(C!11, D!12))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.91/1.12 tff(174,plain,
% 0.91/1.12 (~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[173, 170, 169])).
% 0.91/1.12 tff(175,plain,
% 0.91/1.12 ((~(ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))) | ilf_type(B!10, subset_type(cross_product(C!11, D!12))) | (~ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))),
% 0.91/1.12 inference(tautology,[status(thm)],[])).
% 0.91/1.12 tff(176,plain,
% 0.91/1.12 ((~(ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))) | (~ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.91/1.12 tff(177,plain,
% 0.91/1.12 (~ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[176, 140])).
% 0.91/1.12 tff(178,plain,
% 0.91/1.12 ((~(ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12))))) | ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) | (~member(B!10, power_set(cross_product(C!11, D!12))))),
% 0.91/1.12 inference(tautology,[status(thm)],[])).
% 0.91/1.12 tff(179,plain,
% 0.91/1.12 ((~(ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12))))) | (~member(B!10, power_set(cross_product(C!11, D!12))))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.91/1.12 tff(180,plain,
% 0.91/1.12 (~member(B!10, power_set(cross_product(C!11, D!12)))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[179, 119])).
% 0.91/1.12 tff(181,plain,
% 0.91/1.12 ((~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))) | (~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))),
% 0.91/1.12 inference(tautology,[status(thm)],[])).
% 0.91/1.12 tff(182,plain,
% 0.91/1.12 (~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[181, 180, 70])).
% 0.91/1.12 tff(183,plain,
% 0.91/1.12 ((member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10))) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)),
% 0.91/1.12 inference(tautology,[status(thm)],[])).
% 0.91/1.12 tff(184,plain,
% 0.91/1.12 (member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.91/1.12 tff(185,plain,
% 0.91/1.12 ((member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10))) | ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)),
% 0.91/1.12 inference(tautology,[status(thm)],[])).
% 0.91/1.12 tff(186,plain,
% 0.91/1.12 (ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[185, 182])).
% 0.91/1.12 tff(187,plain,
% 0.91/1.12 ((member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10))) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))),
% 0.91/1.12 inference(tautology,[status(thm)],[])).
% 0.91/1.12 tff(188,plain,
% 0.91/1.12 (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[187, 182])).
% 0.91/1.12 tff(189,plain,
% 0.91/1.12 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 0.91/1.12 inference(bind,[status(th)],[])).
% 0.91/1.12 tff(190,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.12 inference(quant_intro,[status(thm)],[189])).
% 0.91/1.12 tff(191,plain,
% 0.91/1.12 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 0.91/1.12 inference(bind,[status(th)],[])).
% 0.91/1.12 tff(192,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.12 inference(quant_intro,[status(thm)],[191])).
% 0.91/1.12 tff(193,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.12 inference(transitivity,[status(thm)],[192, 190])).
% 0.91/1.12 tff(194,plain,
% 0.91/1.12 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 0.91/1.12 inference(bind,[status(th)],[])).
% 0.91/1.12 tff(195,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.12 inference(quant_intro,[status(thm)],[194])).
% 0.91/1.12 tff(196,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(197,plain,
% 0.91/1.12 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))) <=> (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))), ((ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), rewrite((ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) <=> ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))), ((ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))))), (![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))))),
% 0.91/1.12 inference(bind,[status(th)],[])).
% 0.91/1.12 tff(198,plain,
% 0.91/1.12 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 0.91/1.12 inference(quant_intro,[status(thm)],[197])).
% 0.91/1.12 tff(199,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5')).
% 0.91/1.12 tff(200,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.91/1.12 tff(201,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.91/1.12 tff(202,plain,(
% 0.91/1.12 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))),
% 0.91/1.12 inference(skolemize,[status(sab)],[201])).
% 0.91/1.12 tff(203,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.91/1.12 tff(204,plain,
% 0.91/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[203, 193])).
% 0.91/1.12 tff(205,plain,
% 0.91/1.12 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C)))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C)))))))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(206,plain,
% 0.91/1.12 (((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(subset(B!10, C) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) <=> ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C)))))))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(207,plain,
% 0.91/1.12 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(subset(B!10, C) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[206])).
% 0.91/1.12 tff(208,plain,
% 0.91/1.12 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(subset(B!10, C) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C)))))))),
% 0.91/1.12 inference(transitivity,[status(thm)],[207, 205])).
% 0.91/1.12 tff(209,plain,
% 0.91/1.12 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(subset(B!10, C) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(210,plain,
% 0.91/1.12 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.91/1.12 tff(211,plain,
% 0.91/1.12 (![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[210, 204, 38])).
% 0.91/1.12 tff(212,plain,
% 0.91/1.12 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(213,plain,
% 0.91/1.12 (((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))) | subset(B!10, cross_product(C!11, D!12))))))) <=> ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(214,plain,
% 0.91/1.12 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))) | subset(B!10, cross_product(C!11, D!12)))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12))))))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[213])).
% 0.91/1.13 tff(215,plain,
% 0.91/1.13 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))) | subset(B!10, cross_product(C!11, D!12)))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))),
% 0.91/1.13 inference(transitivity,[status(thm)],[214, 212])).
% 0.91/1.13 tff(216,plain,
% 0.91/1.13 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))) | subset(B!10, cross_product(C!11, D!12)))))))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(217,plain,
% 0.91/1.13 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~((~member(tptp_fun_D_3(C, B!10), B!10)) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | member(tptp_fun_D_3(C, B!10), C))) | subset(B!10, C))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12))))))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.91/1.13 tff(218,plain,
% 0.91/1.13 (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[217, 211, 37])).
% 0.91/1.13 tff(219,plain,
% 0.91/1.13 (((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12))))) | ((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))),
% 0.91/1.13 inference(tautology,[status(thm)],[])).
% 0.91/1.13 tff(220,plain,
% 0.91/1.13 ((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.91/1.13 tff(221,plain,
% 0.91/1.13 (subset(B!10, cross_product(C!11, D!12))),
% 0.91/1.13 inference(or_elim,[status(thm)],[32])).
% 0.91/1.13 tff(222,plain,
% 0.91/1.13 ((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))),
% 0.91/1.13 inference(tautology,[status(thm)],[])).
% 0.91/1.13 tff(223,plain,
% 0.91/1.13 ((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.91/1.13 tff(224,plain,
% 0.91/1.13 (![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[223, 220])).
% 0.91/1.13 tff(225,plain,
% 0.91/1.13 (((~![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))) | ((~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))) <=> ((~![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(226,plain,
% 0.91/1.13 ((~![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))) | ((~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(227,plain,
% 0.91/1.13 ((~![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.91/1.13 tff(228,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[227, 224, 188, 186, 184])).
% 0.91/1.13 % SZS output end Proof
% 0.91/1.13 % E exiting
%------------------------------------------------------------------------------