%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET658+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:26:06 AM UTC 2025
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET658+3 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:34:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(subset_type, type, (
% 0.21/0.42 subset: ( $i * $i ) > $o)).
% 0.21/0.42 tff(domain_of_type, type, (
% 0.21/0.42 domain_of: $i > $i)).
% 0.21/0.42 tff(tptp_fun_B_11_type, type, (
% 0.21/0.42 tptp_fun_B_11: $i)).
% 0.21/0.42 tff(ilf_type_type, type, (
% 0.21/0.42 ilf_type: ( $i * $i ) > $o)).
% 0.21/0.42 tff(relation_type_type, type, (
% 0.21/0.42 relation_type: ( $i * $i ) > $i)).
% 0.21/0.42 tff(range_of_type, type, (
% 0.21/0.42 range_of: $i > $i)).
% 0.21/0.42 tff(binary_relation_type_type, type, (
% 0.21/0.42 binary_relation_type: $i)).
% 0.21/0.42 tff(set_type_type, type, (
% 0.21/0.42 set_type: $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 ((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))) <=> (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 ((~![B: $i] : (ilf_type(B, binary_relation_type) => ilf_type(B, relation_type(domain_of(B), range_of(B))))) <=> (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(3,axiom,(~![B: $i] : (ilf_type(B, binary_relation_type) => ilf_type(B, relation_type(domain_of(B), range_of(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_relset_1_20')).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.42 tff(8,plain,(
% 0.21/0.42 ~((~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[7])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (ilf_type(B!11, binary_relation_type)),
% 0.21/0.42 inference(or_elim,[status(thm)],[8])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (^[B: $i] : refl(((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)) <=> ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)) <=> ![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)) <=> ![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (^[B: $i] : rewrite((ilf_type(B, binary_relation_type) => ilf_type(domain_of(B), set_type)) <=> ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![B: $i] : (ilf_type(B, binary_relation_type) => ilf_type(domain_of(B), set_type)) <=> ![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.42 tff(15,axiom,(![B: $i] : (ilf_type(B, binary_relation_type) => ilf_type(domain_of(B), set_type))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3')).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.42 tff(18,plain,(
% 0.21/0.42 ![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.21/0.42 inference(skolemize,[status(sab)],[17])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))) | ((~ilf_type(B!11, binary_relation_type)) | ilf_type(domain_of(B!11), set_type))) <=> ((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))) | (~ilf_type(B!11, binary_relation_type)) | ilf_type(domain_of(B!11), set_type))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 ((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))) | ((~ilf_type(B!11, binary_relation_type)) | ilf_type(domain_of(B!11), set_type))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 ((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))) | (~ilf_type(B!11, binary_relation_type)) | ilf_type(domain_of(B!11), set_type)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (ilf_type(domain_of(B!11), set_type)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[27, 25])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C)))) <=> ((~subset(domain_of(C), B)) | ilf_type(C, relation_type(B, range_of(C))))), ((ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))) <=> (ilf_type(C, binary_relation_type) => ((~subset(domain_of(C), B)) | ilf_type(C, relation_type(B, range_of(C))))))), rewrite((ilf_type(C, binary_relation_type) => ((~subset(domain_of(C), B)) | ilf_type(C, relation_type(B, range_of(C))))) <=> (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))), ((ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))) <=> (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))))), (![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))) <=> ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C)))))) <=> (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))))), rewrite((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.42 tff(32,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p1')).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.42 tff(35,plain,(
% 0.21/0.42 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[34])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11)))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | (~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : (ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))) | (~ilf_type(C, binary_relation_type)))) <=> ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : (ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))) | (~ilf_type(C, binary_relation_type))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : (ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))) | (~ilf_type(C, binary_relation_type))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | (~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11)))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[39, 37])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : (ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))) | (~ilf_type(C, binary_relation_type))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | (~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[42, 36, 23])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (^[B: $i] : refl(((~ilf_type(B, set_type)) | subset(B, B)) <=> ((~ilf_type(B, set_type)) | subset(B, B)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (^[B: $i] : rewrite((ilf_type(B, set_type) => subset(B, B)) <=> ((~ilf_type(B, set_type)) | subset(B, B)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (![B: $i] : (ilf_type(B, set_type) => subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.43 tff(49,axiom,(![B: $i] : (ilf_type(B, set_type) => subset(B, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15')).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.43 tff(52,plain,(
% 0.21/0.43 ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.21/0.43 inference(skolemize,[status(sab)],[51])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | ((~ilf_type(domain_of(B!11), set_type)) | subset(domain_of(B!11), domain_of(B!11)))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | (~ilf_type(domain_of(B!11), set_type)) | subset(domain_of(B!11), domain_of(B!11)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | ((~ilf_type(domain_of(B!11), set_type)) | subset(domain_of(B!11), domain_of(B!11)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | (~ilf_type(domain_of(B!11), set_type)) | subset(domain_of(B!11), domain_of(B!11))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (subset(domain_of(B!11), domain_of(B!11))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[56, 53, 23])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (~ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11)))),
% 0.21/0.43 inference(or_elim,[status(thm)],[8])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (((~![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))) | ((~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))) | (~subset(domain_of(B!11), domain_of(B!11))))) <=> ((~![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))) | (~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))) | (~subset(domain_of(B!11), domain_of(B!11))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 ((~![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))) | ((~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))) | (~subset(domain_of(B!11), domain_of(B!11))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 ((~![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))) | (~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))) | (~subset(domain_of(B!11), domain_of(B!11)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[61, 9, 58, 57, 43])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------