TSTP Solution File: SEU041+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU041+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Tue Sep 20 07:27:22 EDT 2022
% Result : Theorem 1.12s 0.95s
% Output : Proof 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU041+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Sep 3 09:07:50 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 1.12/0.95 % SZS status Theorem
% 1.12/0.95 % SZS output start Proof
% 1.12/0.95 tff(relation_type, type, (
% 1.12/0.95 relation: $i > $o)).
% 1.12/0.95 tff(subset_type, type, (
% 1.12/0.95 subset: ( $i * $i ) > $o)).
% 1.12/0.95 tff(relation_dom_restriction_type, type, (
% 1.12/0.95 relation_dom_restriction: ( $i * $i ) > $i)).
% 1.12/0.95 tff(tptp_fun_C_11_type, type, (
% 1.12/0.95 tptp_fun_C_11: $i)).
% 1.12/0.95 tff(function_type, type, (
% 1.12/0.95 function: $i > $o)).
% 1.12/0.95 tff(tptp_fun_B_12_type, type, (
% 1.12/0.95 tptp_fun_B_12: $i)).
% 1.12/0.95 tff(tptp_fun_A_13_type, type, (
% 1.12/0.95 tptp_fun_A_13: $i)).
% 1.12/0.95 tff(1,plain,
% 1.12/0.95 (^[A: $i, B: $i, C: $i] : refl(((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(2,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[1])).
% 1.12/0.95 tff(3,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(4,plain,
% 1.12/0.95 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A))) <=> ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))), ((relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))) <=> (relation(C) => ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))))), rewrite((relation(C) => ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))) <=> ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))), ((relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))) <=> ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(5,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[4])).
% 1.12/0.95 tff(6,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t102_relat_1')).
% 1.12/0.95 tff(7,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.12/0.95 tff(8,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.12/0.95 tff(9,plain,(
% 1.12/0.95 ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(skolemize,[status(sab)],[8])).
% 1.12/0.95 tff(10,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.12/0.95 tff(11,plain,
% 1.12/0.95 ((~(((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) | (~subset(A!13, B!12)) | (~(relation(C!11) & function(C!11))))) <=> (~(((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) | (~subset(A!13, B!12)) | (~(relation(C!11) & function(C!11)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(12,plain,
% 1.12/0.95 ((~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))) <=> (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(13,plain,
% 1.12/0.95 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (subset(A, B) => ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))))) <=> (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C)))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(14,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (subset(A, B) => ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t82_funct_1')).
% 1.12/0.95 tff(15,plain,
% 1.12/0.95 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.12/0.95 tff(16,plain,
% 1.12/0.95 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[15, 12])).
% 1.12/0.95 tff(17,plain,
% 1.12/0.95 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.12/0.95 tff(18,plain,
% 1.12/0.95 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[17, 12])).
% 1.12/0.95 tff(19,plain,
% 1.12/0.95 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[18, 12])).
% 1.12/0.95 tff(20,plain,
% 1.12/0.95 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.12/0.95 tff(21,plain,
% 1.12/0.95 (~![A: $i, B: $i, C: $i] : (((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) & (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) | (~subset(A, B)) | (~(relation(C) & function(C))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[20, 12])).
% 1.12/0.95 tff(22,plain,(
% 1.12/0.95 ~(((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) | (~subset(A!13, B!12)) | (~(relation(C!11) & function(C!11))))),
% 1.12/0.95 inference(skolemize,[status(sab)],[21])).
% 1.12/0.95 tff(23,plain,
% 1.12/0.95 (~(((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) | (~subset(A!13, B!12)) | (~(relation(C!11) & function(C!11))))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[22, 11])).
% 1.12/0.95 tff(24,plain,
% 1.12/0.95 (relation(C!11) & function(C!11)),
% 1.12/0.95 inference(or_elim,[status(thm)],[23])).
% 1.12/0.95 tff(25,plain,
% 1.12/0.95 (relation(C!11)),
% 1.12/0.95 inference(and_elim,[status(thm)],[24])).
% 1.12/0.95 tff(26,plain,
% 1.12/0.95 (subset(A!13, B!12)),
% 1.12/0.95 inference(or_elim,[status(thm)],[23])).
% 1.12/0.95 tff(27,plain,
% 1.12/0.95 (^[A: $i, B: $i, C: $i] : refl(((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(28,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[27])).
% 1.12/0.95 tff(29,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(30,plain,
% 1.12/0.95 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))) <=> ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))), ((relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))) <=> (relation(C) => ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))))), rewrite((relation(C) => ((~subset(A, B)) | (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))) <=> ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))), ((relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))) <=> ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))))),
% 1.12/0.95 inference(bind,[status(th)],[])).
% 1.12/0.95 tff(31,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)))) <=> ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(quant_intro,[status(thm)],[30])).
% 1.12/0.95 tff(32,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => (relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t103_relat_1')).
% 1.12/0.95 tff(33,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.12/0.95 tff(34,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.12/0.95 tff(35,plain,(
% 1.12/0.95 ![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(skolemize,[status(sab)],[34])).
% 1.12/0.95 tff(36,plain,
% 1.12/0.95 (![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[35, 28])).
% 1.12/0.95 tff(37,assumption,(~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))), introduced(assumption)).
% 1.12/0.95 tff(38,plain,
% 1.12/0.95 (((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | ((relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(39,plain,
% 1.12/0.95 ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | ((relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 1.12/0.95 inference(quant_inst,[status(thm)],[])).
% 1.12/0.95 tff(40,plain,
% 1.12/0.95 ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, B), A) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11))),
% 1.12/0.95 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.12/0.95 tff(41,plain,
% 1.12/0.95 ($false),
% 1.12/0.95 inference(unit_resolution,[status(thm)],[40, 37, 26, 25, 36])).
% 1.12/0.95 tff(42,plain,(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)), inference(lemma,lemma(discharge,[]))).
% 1.12/0.95 tff(43,plain,
% 1.12/0.95 ((~(~((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))))) <=> ((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))))),
% 1.12/0.95 inference(rewrite,[status(thm)],[])).
% 1.12/0.95 tff(44,plain,
% 1.12/0.95 (((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))) <=> (~((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(45,plain,
% 1.12/0.96 ((~((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))) <=> (~(~((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))))))),
% 1.12/0.96 inference(monotonicity,[status(thm)],[44])).
% 1.12/0.96 tff(46,plain,
% 1.12/0.96 ((~((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))) <=> ((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13))))),
% 1.12/0.96 inference(transitivity,[status(thm)],[45, 43])).
% 1.12/0.96 tff(47,plain,
% 1.12/0.96 (~((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) & (relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))),
% 1.12/0.96 inference(or_elim,[status(thm)],[23])).
% 1.12/0.96 tff(48,plain,
% 1.12/0.96 ((~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))) | (~(relation_dom_restriction(relation_dom_restriction(C!11, B!12), A!13) = relation_dom_restriction(C!11, A!13)))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.12/0.96 tff(49,plain,
% 1.12/0.96 (~(relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13))),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[48, 42])).
% 1.12/0.96 tff(50,plain,
% 1.12/0.96 (((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | ((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | (relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 1.12/0.96 inference(rewrite,[status(thm)],[])).
% 1.12/0.96 tff(51,plain,
% 1.12/0.96 ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | ((relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11)))),
% 1.12/0.96 inference(quant_inst,[status(thm)],[])).
% 1.12/0.96 tff(52,plain,
% 1.12/0.96 ((~![A: $i, B: $i, C: $i] : ((relation_dom_restriction(relation_dom_restriction(C, A), B) = relation_dom_restriction(C, A)) | (~subset(A, B)) | (~relation(C)))) | (relation_dom_restriction(relation_dom_restriction(C!11, A!13), B!12) = relation_dom_restriction(C!11, A!13)) | (~subset(A!13, B!12)) | (~relation(C!11))),
% 1.12/0.96 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.12/0.96 tff(53,plain,
% 1.12/0.96 ($false),
% 1.12/0.96 inference(unit_resolution,[status(thm)],[52, 49, 26, 25, 10])).
% 1.12/0.96 % SZS output end Proof
%------------------------------------------------------------------------------