%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU047+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:26:50 AM UTC 2025
% Result : Theorem 0.83s 1.00s
% Output : Proof 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SEU047+1 : TPTP v9.0.0. Released v3.2.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 05:58:10 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.83/1.00 % SZS status Theorem
% 0.83/1.00 % SZS output start Proof
% 0.83/1.00 tff(subset_type, type, (
% 0.83/1.00 subset: ( $i * $i ) > $o)).
% 0.83/1.00 tff(relation_type, type, (
% 0.83/1.00 relation: $i > $o)).
% 0.83/1.00 tff(relation_rng_restriction_type, type, (
% 0.83/1.00 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.83/1.00 tff(tptp_fun_B_12_type, type, (
% 0.83/1.00 tptp_fun_B_12: $i)).
% 0.83/1.00 tff(tptp_fun_A_13_type, type, (
% 0.83/1.00 tptp_fun_A_13: $i)).
% 0.83/1.00 tff(function_type, type, (
% 0.83/1.00 function: $i > $o)).
% 0.83/1.00 tff(tptp_fun_C_11_type, type, (
% 0.83/1.00 tptp_fun_C_11: $i)).
% 0.83/1.00 tff(1,plain,
% 0.83/1.00 (^[A: $i, B: $i, C: $i] : refl(((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B))) <=> ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B))))),
% 0.83/1.00 inference(bind,[status(th)],[])).
% 0.83/1.00 tff(2,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(quant_intro,[status(thm)],[1])).
% 0.83/1.00 tff(3,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(4,plain,
% 0.83/1.00 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((subset(A, B) => (relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C))) <=> ((~subset(A, B)) | (relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)))), ((relation(C) => (subset(A, B) => (relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)))) <=> (relation(C) => ((~subset(A, B)) | (relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)))))), rewrite((relation(C) => ((~subset(A, B)) | (relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)))) <=> ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))), ((relation(C) => (subset(A, B) => (relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)))) <=> ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))))),
% 0.83/1.00 inference(bind,[status(th)],[])).
% 0.83/1.00 tff(5,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)))) <=> ![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(quant_intro,[status(thm)],[4])).
% 0.83/1.00 tff(6,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t129_relat_1')).
% 0.83/1.00 tff(7,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.83/1.00 tff(8,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.83/1.00 tff(9,plain,(
% 0.83/1.00 ![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(skolemize,[status(sab)],[8])).
% 0.83/1.00 tff(10,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.83/1.00 tff(11,plain,
% 0.83/1.00 ((~(((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) & (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation(C!11) & function(C!11))) | (~subset(A!13, B!12)))) <=> (~(((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) & (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation(C!11) & function(C!11))) | (~subset(A!13, B!12))))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(12,plain,
% 0.83/1.00 ((~![A: $i, B: $i, C: $i] : (((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))) | (~(relation(C) & function(C))) | (~subset(A, B)))) <=> (~![A: $i, B: $i, C: $i] : (((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))) | (~(relation(C) & function(C))) | (~subset(A, B))))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(13,plain,
% 0.83/1.00 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (subset(A, B) => ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)))))) <=> (~![A: $i, B: $i, C: $i] : (((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))) | (~(relation(C) & function(C))) | (~subset(A, B))))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(14,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (subset(A, B) => ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t97_funct_1')).
% 0.83/1.00 tff(15,plain,
% 0.83/1.00 (~![A: $i, B: $i, C: $i] : (((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))) | (~(relation(C) & function(C))) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.83/1.00 tff(16,plain,
% 0.83/1.00 (~![A: $i, B: $i, C: $i] : (((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))) | (~(relation(C) & function(C))) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.83/1.00 tff(17,plain,
% 0.83/1.00 (~![A: $i, B: $i, C: $i] : (((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))) | (~(relation(C) & function(C))) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.83/1.00 tff(18,plain,
% 0.83/1.00 (~![A: $i, B: $i, C: $i] : (((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) & (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))) | (~(relation(C) & function(C))) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.83/1.00 tff(19,plain,(
% 0.83/1.00 ~(((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) & (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation(C!11) & function(C!11))) | (~subset(A!13, B!12)))),
% 0.83/1.00 inference(skolemize,[status(sab)],[18])).
% 0.83/1.00 tff(20,plain,
% 0.83/1.00 (~(((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) & (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation(C!11) & function(C!11))) | (~subset(A!13, B!12)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.83/1.00 tff(21,plain,
% 0.83/1.00 (subset(A!13, B!12)),
% 0.83/1.00 inference(or_elim,[status(thm)],[20])).
% 0.83/1.00 tff(22,plain,
% 0.83/1.00 (relation(C!11) & function(C!11)),
% 0.83/1.00 inference(or_elim,[status(thm)],[20])).
% 0.83/1.00 tff(23,plain,
% 0.83/1.00 (relation(C!11)),
% 0.83/1.00 inference(and_elim,[status(thm)],[22])).
% 0.83/1.00 tff(24,plain,
% 0.83/1.00 (^[A: $i, B: $i, C: $i] : refl(((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B))) <=> ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B))))),
% 0.83/1.00 inference(bind,[status(th)],[])).
% 0.83/1.00 tff(25,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(quant_intro,[status(thm)],[24])).
% 0.83/1.00 tff(26,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(27,plain,
% 0.83/1.00 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((subset(A, B) => (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))) <=> ((~subset(A, B)) | (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)))), ((relation(C) => (subset(A, B) => (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)))) <=> (relation(C) => ((~subset(A, B)) | (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)))))), rewrite((relation(C) => ((~subset(A, B)) | (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)))) <=> ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))), ((relation(C) => (subset(A, B) => (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)))) <=> ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))))),
% 0.83/1.00 inference(bind,[status(th)],[])).
% 0.83/1.00 tff(28,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)))) <=> ![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(quant_intro,[status(thm)],[27])).
% 0.83/1.00 tff(29,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t130_relat_1')).
% 0.83/1.00 tff(30,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.83/1.00 tff(31,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.83/1.00 tff(32,plain,(
% 0.83/1.00 ![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(skolemize,[status(sab)],[31])).
% 0.83/1.00 tff(33,plain,
% 0.83/1.00 (![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.83/1.00 tff(34,assumption,(~(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))), introduced(assumption)).
% 0.83/1.00 tff(35,plain,
% 0.83/1.00 (((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(36,plain,
% 0.83/1.00 (((relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~relation(C!11)) | (~subset(A!13, B!12))) <=> ((relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(37,plain,
% 0.83/1.00 (((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~relation(C!11)) | (~subset(A!13, B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11))))),
% 0.83/1.00 inference(monotonicity,[status(thm)],[36])).
% 0.83/1.00 tff(38,plain,
% 0.83/1.00 (((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~relation(C!11)) | (~subset(A!13, B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.83/1.00 inference(transitivity,[status(thm)],[37, 35])).
% 0.83/1.00 tff(39,plain,
% 0.83/1.00 ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~relation(C!11)) | (~subset(A!13, B!12)))),
% 0.83/1.00 inference(quant_inst,[status(thm)],[])).
% 0.83/1.00 tff(40,plain,
% 0.83/1.00 ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.83/1.00 tff(41,plain,
% 0.83/1.00 ($false),
% 0.83/1.00 inference(unit_resolution,[status(thm)],[40, 34, 23, 21, 33])).
% 0.83/1.00 tff(42,plain,(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)), inference(lemma,lemma(discharge,[]))).
% 0.83/1.00 tff(43,plain,
% 0.83/1.00 ((~(~((~(relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)))))) <=> ((~(relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(44,plain,
% 0.83/1.00 (((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) & (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))) <=> (~((~(relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)))))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(45,plain,
% 0.83/1.00 ((~((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) & (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)))) <=> (~(~((~(relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))))))),
% 0.83/1.00 inference(monotonicity,[status(thm)],[44])).
% 0.83/1.00 tff(46,plain,
% 0.83/1.00 ((~((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) & (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)))) <=> ((~(relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))))),
% 0.83/1.00 inference(transitivity,[status(thm)],[45, 43])).
% 0.83/1.00 tff(47,plain,
% 0.83/1.00 (~((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) & (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)))),
% 0.83/1.00 inference(or_elim,[status(thm)],[20])).
% 0.83/1.00 tff(48,plain,
% 0.83/1.00 ((~(relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11))) | (~(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)))),
% 0.83/1.00 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.83/1.00 tff(49,plain,
% 0.83/1.00 (~(relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11))),
% 0.83/1.00 inference(unit_resolution,[status(thm)],[48, 42])).
% 0.83/1.00 tff(50,plain,
% 0.83/1.00 (((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | (relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(51,plain,
% 0.83/1.00 (((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~relation(C!11)) | (~subset(A!13, B!12))) <=> ((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.83/1.00 inference(rewrite,[status(thm)],[])).
% 0.83/1.00 tff(52,plain,
% 0.83/1.00 (((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~relation(C!11)) | (~subset(A!13, B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11))))),
% 0.83/1.01 inference(monotonicity,[status(thm)],[51])).
% 0.83/1.01 tff(53,plain,
% 0.83/1.01 (((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~relation(C!11)) | (~subset(A!13, B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | (relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 0.83/1.01 inference(transitivity,[status(thm)],[52, 50])).
% 0.83/1.01 tff(54,plain,
% 0.83/1.01 ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | ((relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~relation(C!11)) | (~subset(A!13, B!12)))),
% 0.83/1.01 inference(quant_inst,[status(thm)],[])).
% 0.83/1.01 tff(55,plain,
% 0.83/1.01 ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | (relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11))),
% 0.83/1.01 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.83/1.01 tff(56,plain,
% 0.83/1.01 ($false),
% 0.83/1.01 inference(unit_resolution,[status(thm)],[55, 49, 23, 21, 10])).
% 0.83/1.01 % SZS output end Proof
% 0.83/1.01 % E exiting
%------------------------------------------------------------------------------