TSTP Solution File: SEU047+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU047+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 07:27:23 EDT 2022
% Result : Theorem 1.55s 1.25s
% Output : Proof 1.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU047+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 09:27:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.55/1.25 % SZS status Theorem
% 1.55/1.25 % SZS output start Proof
% 1.55/1.25 tff(subset_type, type, (
% 1.55/1.25 subset: ( $i * $i ) > $o)).
% 1.55/1.25 tff(relation_type, type, (
% 1.55/1.25 relation: $i > $o)).
% 1.55/1.25 tff(relation_rng_restriction_type, type, (
% 1.55/1.25 relation_rng_restriction: ( $i * $i ) > $i)).
% 1.55/1.25 tff(tptp_fun_B_12_type, type, (
% 1.55/1.25 tptp_fun_B_12: $i)).
% 1.55/1.25 tff(tptp_fun_A_13_type, type, (
% 1.55/1.25 tptp_fun_A_13: $i)).
% 1.55/1.25 tff(function_type, type, (
% 1.55/1.25 function: $i > $o)).
% 1.55/1.25 tff(tptp_fun_C_11_type, type, (
% 1.55/1.25 tptp_fun_C_11: $i)).
% 1.55/1.25 tff(1,plain,
% 1.55/1.25 (^[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))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(2,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[1])).
% 1.55/1.25 tff(3,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(4,plain,
% 1.55/1.25 (^[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)))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(5,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[4])).
% 1.55/1.25 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/sandbox2/benchmark/theBenchmark.p','t129_relat_1')).
% 1.55/1.25 tff(7,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.55/1.25 tff(8,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.55/1.25 tff(9,plain,(
% 1.55/1.25 ![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)))),
% 1.55/1.25 inference(skolemize,[status(sab)],[8])).
% 1.55/1.25 tff(10,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.55/1.25 tff(11,plain,
% 1.55/1.25 ((~(((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))))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(12,plain,
% 1.55/1.25 ((~![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))))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(13,plain,
% 1.55/1.25 ((~![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))))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 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/sandbox2/benchmark/theBenchmark.p','t97_funct_1')).
% 1.55/1.25 tff(15,plain,
% 1.55/1.25 (~![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.55/1.25 tff(16,plain,
% 1.55/1.25 (~![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[15, 12])).
% 1.55/1.25 tff(17,plain,
% 1.55/1.25 (~![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.55/1.25 tff(18,plain,
% 1.55/1.25 (~![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[17, 12])).
% 1.55/1.25 tff(19,plain,
% 1.55/1.25 (~![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[18, 12])).
% 1.55/1.25 tff(20,plain,
% 1.55/1.25 (~![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.55/1.25 tff(21,plain,
% 1.55/1.25 (~![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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[20, 12])).
% 1.55/1.25 tff(22,plain,(
% 1.55/1.25 ~(((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)))),
% 1.55/1.25 inference(skolemize,[status(sab)],[21])).
% 1.55/1.25 tff(23,plain,
% 1.55/1.25 (~(((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)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[22, 11])).
% 1.55/1.25 tff(24,plain,
% 1.55/1.25 (subset(A!13, B!12)),
% 1.55/1.25 inference(or_elim,[status(thm)],[23])).
% 1.55/1.25 tff(25,plain,
% 1.55/1.25 (relation(C!11) & function(C!11)),
% 1.55/1.25 inference(or_elim,[status(thm)],[23])).
% 1.55/1.25 tff(26,plain,
% 1.55/1.25 (relation(C!11)),
% 1.55/1.25 inference(and_elim,[status(thm)],[25])).
% 1.55/1.25 tff(27,plain,
% 1.55/1.25 (^[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))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(28,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[27])).
% 1.55/1.25 tff(29,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(30,plain,
% 1.55/1.25 (^[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)))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(31,plain,
% 1.55/1.25 (![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)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[30])).
% 1.55/1.26 tff(32,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/sandbox2/benchmark/theBenchmark.p','t130_relat_1')).
% 1.55/1.26 tff(33,plain,
% 1.55/1.26 (![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)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.55/1.26 tff(34,plain,
% 1.55/1.26 (![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)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.55/1.26 tff(35,plain,(
% 1.55/1.26 ![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)))),
% 1.55/1.26 inference(skolemize,[status(sab)],[34])).
% 1.55/1.26 tff(36,plain,
% 1.55/1.26 (![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)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[35, 28])).
% 1.55/1.26 tff(37,assumption,(~(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11))), introduced(assumption)).
% 1.55/1.26 tff(38,plain,
% 1.55/1.26 (((~![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)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(39,plain,
% 1.55/1.26 (((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)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(40,plain,
% 1.55/1.26 (((~![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))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[39])).
% 1.55/1.26 tff(41,plain,
% 1.55/1.26 (((~![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)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[40, 38])).
% 1.55/1.26 tff(42,plain,
% 1.55/1.26 ((~![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)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(43,plain,
% 1.55/1.26 ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(A, relation_rng_restriction(B, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | (relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.55/1.26 tff(44,plain,
% 1.55/1.26 ($false),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[43, 37, 26, 24, 36])).
% 1.55/1.26 tff(45,plain,(relation_rng_restriction(A!13, relation_rng_restriction(B!12, C!11)) = relation_rng_restriction(A!13, C!11)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.26 tff(46,plain,
% 1.55/1.26 ((~(~((~(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))))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(47,plain,
% 1.55/1.26 (((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)))))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(48,plain,
% 1.55/1.26 ((~((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))))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[47])).
% 1.55/1.26 tff(49,plain,
% 1.55/1.26 ((~((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))))),
% 1.55/1.26 inference(transitivity,[status(thm)],[48, 46])).
% 1.55/1.26 tff(50,plain,
% 1.55/1.26 (~((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)))),
% 1.55/1.26 inference(or_elim,[status(thm)],[23])).
% 1.55/1.26 tff(51,plain,
% 1.55/1.26 ((~(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)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.55/1.26 tff(52,plain,
% 1.55/1.26 (~(relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[51, 45])).
% 1.55/1.26 tff(53,plain,
% 1.55/1.26 (((~![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)))),
% 1.62/1.27 inference(rewrite,[status(thm)],[])).
% 1.62/1.27 tff(54,plain,
% 1.62/1.27 (((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)))),
% 1.62/1.27 inference(rewrite,[status(thm)],[])).
% 1.62/1.27 tff(55,plain,
% 1.62/1.27 (((~![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))))),
% 1.62/1.27 inference(monotonicity,[status(thm)],[54])).
% 1.62/1.27 tff(56,plain,
% 1.62/1.27 (((~![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)))),
% 1.62/1.27 inference(transitivity,[status(thm)],[55, 53])).
% 1.62/1.27 tff(57,plain,
% 1.62/1.27 ((~![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)))),
% 1.62/1.27 inference(quant_inst,[status(thm)],[])).
% 1.62/1.27 tff(58,plain,
% 1.62/1.27 ((~![A: $i, B: $i, C: $i] : ((relation_rng_restriction(B, relation_rng_restriction(A, C)) = relation_rng_restriction(A, C)) | (~relation(C)) | (~subset(A, B)))) | (relation_rng_restriction(B!12, relation_rng_restriction(A!13, C!11)) = relation_rng_restriction(A!13, C!11)) | (~subset(A!13, B!12)) | (~relation(C!11))),
% 1.62/1.27 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.62/1.27 tff(59,plain,
% 1.62/1.27 ($false),
% 1.62/1.27 inference(unit_resolution,[status(thm)],[58, 52, 26, 24, 10])).
% 1.62/1.27 % SZS output end Proof
%------------------------------------------------------------------------------