TSTP Solution File: NUM841+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM841+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 : Sun Sep 18 13:12:12 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM841+1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 15:32:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(less_type, type, (
% 0.19/0.41 less: ( $i * $i ) > $o)).
% 0.19/0.41 tff(vplus_type, type, (
% 0.19/0.41 vplus: ( $i * $i ) > $i)).
% 0.19/0.41 tff(vd347_type, type, (
% 0.19/0.41 vd347: $i)).
% 0.19/0.41 tff(vd344_type, type, (
% 0.19/0.41 vd344: $i)).
% 0.19/0.41 tff(vd345_type, type, (
% 0.19/0.41 vd345: $i)).
% 0.19/0.41 tff(greater_type, type, (
% 0.19/0.41 greater: ( $i * $i ) > $o)).
% 0.19/0.41 tff(vd348_type, type, (
% 0.19/0.41 vd348: $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[Vd208: $i, Vd209: $i] : refl(((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (^[Vd208: $i, Vd209: $i] : rewrite((greater(Vd208, Vd209) => less(Vd209, Vd208)) <=> ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![Vd208: $i, Vd209: $i] : (greater(Vd208, Vd209) => less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.41 tff(6,axiom,(![Vd208: $i, Vd209: $i] : (greater(Vd208, Vd209) => less(Vd209, Vd208))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(140, 0), 0)'')).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,(
% 0.19/0.41 ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.19/0.41 inference(skolemize,[status(sab)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (greater(vplus(vd344, vd347), vplus(vd345, vd347)) <=> greater(vplus(vd344, vd347), vplus(vd347, vd345))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (greater(vplus(vd344, vd347), vplus(vd345, vd347)) <=> greater(vplus(vd344, vd347), vplus(vd345, vd347))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,axiom,(greater(vplus(vd344, vd347), vplus(vd345, vd347))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(212, 350, 0)'')).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (greater(vplus(vd344, vd347), vplus(vd345, vd347))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (greater(vplus(vd344, vd347), vplus(vd347, vd345))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vplus(vd344, vd347), vplus(vd347, vd345))) | less(vplus(vd347, vd345), vplus(vd344, vd347)))) <=> ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vplus(vd344, vd347), vplus(vd347, vd345))) | less(vplus(vd347, vd345), vplus(vd344, vd347)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vplus(vd344, vd347), vplus(vd347, vd345))) | less(vplus(vd347, vd345), vplus(vd344, vd347)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vplus(vd344, vd347), vplus(vd347, vd345))) | less(vplus(vd347, vd345), vplus(vd344, vd347))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (less(vplus(vd347, vd345), vplus(vd344, vd347))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[18, 15, 10])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (greater(vplus(vd347, vd345), vplus(vd348, vd345)) <=> greater(vplus(vd347, vd345), vplus(vd345, vd348))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (greater(vplus(vd347, vd345), vplus(vd348, vd345)) <=> greater(vplus(vd347, vd345), vplus(vd348, vd345))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,axiom,(greater(vplus(vd347, vd345), vplus(vd348, vd345))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(213, 351, 1)'')).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (greater(vplus(vd347, vd345), vplus(vd348, vd345))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (greater(vplus(vd347, vd345), vplus(vd345, vd348))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vplus(vd347, vd345), vplus(vd345, vd348))) | less(vplus(vd345, vd348), vplus(vd347, vd345)))) <=> ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vplus(vd347, vd345), vplus(vd345, vd348))) | less(vplus(vd345, vd348), vplus(vd347, vd345)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vplus(vd347, vd345), vplus(vd345, vd348))) | less(vplus(vd345, vd348), vplus(vd347, vd345)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vplus(vd347, vd345), vplus(vd345, vd348))) | less(vplus(vd345, vd348), vplus(vd347, vd345))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (less(vplus(vd345, vd348), vplus(vd347, vd345))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[27, 24, 10])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (^[Vd226: $i, Vd227: $i] : refl(((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (^[Vd226: $i, Vd227: $i] : rewrite((less(Vd226, Vd227) => greater(Vd227, Vd226)) <=> ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![Vd226: $i, Vd227: $i] : (less(Vd226, Vd227) => greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,axiom,(![Vd226: $i, Vd227: $i] : (less(Vd226, Vd227) => greater(Vd227, Vd226))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(147, 0), 0)'')).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.41 tff(37,plain,(
% 0.19/0.41 ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.19/0.41 inference(skolemize,[status(sab)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~greater(vplus(vd344, vd347), vplus(vd345, vd348))) <=> (~greater(vplus(vd344, vd347), vplus(vd345, vd348)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,axiom,(~greater(vplus(vd344, vd347), vplus(vd345, vd348))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(214, 352, 0)'')).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (~greater(vplus(vd344, vd347), vplus(vd345, vd348))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | ((~less(vplus(vd345, vd348), vplus(vd344, vd347))) | greater(vplus(vd344, vd347), vplus(vd345, vd348)))) <=> ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | (~less(vplus(vd345, vd348), vplus(vd344, vd347))) | greater(vplus(vd344, vd347), vplus(vd345, vd348)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | ((~less(vplus(vd345, vd348), vplus(vd344, vd347))) | greater(vplus(vd344, vd347), vplus(vd345, vd348)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | (~less(vplus(vd345, vd348), vplus(vd344, vd347))) | greater(vplus(vd344, vd347), vplus(vd345, vd348))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (~less(vplus(vd345, vd348), vplus(vd344, vd347))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 41, 38])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263))) <=> ![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (^[Vd262: $i, Vd263: $i, Vd265: $i] : trans(monotonicity(trans(monotonicity(rewrite((less(Vd263, Vd265) & less(Vd262, Vd263)) <=> (~((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))))), ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) <=> (~(~((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))))))), rewrite((~(~((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))))) <=> ((~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))), ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) <=> ((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))))), (((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> (((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))) | less(Vd262, Vd265)))), rewrite((((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))), (((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> ![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> ![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (^[Vd262: $i, Vd263: $i, Vd265: $i] : rewrite(((less(Vd263, Vd265) & less(Vd262, Vd263)) => less(Vd262, Vd265)) <=> ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((less(Vd263, Vd265) & less(Vd262, Vd263)) => less(Vd262, Vd265)) <=> ![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.41 tff(52,axiom,(![Vd262: $i, Vd263: $i, Vd265: $i] : ((less(Vd263, Vd265) & less(Vd262, Vd263)) => less(Vd262, Vd265))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(168, 0), 0)'')).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.41 tff(55,plain,(
% 0.19/0.41 ![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.19/0.41 inference(skolemize,[status(sab)],[54])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))) | (~less(vplus(vd347, vd345), vplus(vd344, vd347))))) <=> ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))) | (~less(vplus(vd347, vd345), vplus(vd344, vd347))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd347, vd345), vplus(vd344, vd347))) | (~less(vplus(vd345, vd348), vplus(vd347, vd345)))) <=> (less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))) | (~less(vplus(vd347, vd345), vplus(vd344, vd347))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd347, vd345), vplus(vd344, vd347))) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))))) <=> ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))) | (~less(vplus(vd347, vd345), vplus(vd344, vd347)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd347, vd345), vplus(vd344, vd347))) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))))) <=> ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))) | (~less(vplus(vd347, vd345), vplus(vd344, vd347))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd347, vd345), vplus(vd344, vd347))) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | less(vplus(vd345, vd348), vplus(vd344, vd347)) | (~less(vplus(vd345, vd348), vplus(vd347, vd345))) | (~less(vplus(vd347, vd345), vplus(vd344, vd347)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[63, 57, 45, 28, 19])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------