%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP654-12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:35:04 PM UTC 2026
% Result : Unsatisfiable 272.14s 36.48s
% Output : CNFRefutation 272.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 8
% Syntax : Number of formulae : 166 ( 166 unt; 2 def)
% Number of atoms : 556 ( 165 equ)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 193 ( 0 sgn 193 !; 0 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X0,X1] : mult(X0,mult(X1,mult(X0,X2))) = mult(mult(mult(X0,X1),X0),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f7,plain,
x0 != mult(rd(x1,x1),x0),
inference(reorient_equations,[],[f6]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(mult(X0,X1),X0),X2) = mult(X0,mult(X1,mult(X0,X2))),
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,definition,
iPr_def_10 = rd(x1,x1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_84,definition,
iPr_def_11 = mult(iPr_def_10,x0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_85,negated_conjecture,
iPr_def_11 != x0,
inference(demodulation,[status(thm)],[c_60,c_83,c_84]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(mult(X0,X1),X0),X2) = mult(X0,mult(X1,mult(X0,X2))),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : rd(mult(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(mult(mult(X0,mult(X1,mult(X0,X2))),mult(mult(X0,X1),X0)),X3) = mult(mult(mult(X0,X1),X0),mult(X2,mult(mult(mult(X0,X1),X0),X3))),
inference(superposition,[status(thm)],[c_86,c_86]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,mult(X1,mult(X0,mult(X0,X1)))),X2) = mult(mult(X0,X1),mult(X0,mult(mult(X0,X1),X2))),
inference(superposition,[status(thm)],[c_86,c_86]) ).
tcf(c_148,plain,
! [X0: $i] : mult(iPr_def_10,mult(x0,mult(iPr_def_10,X0))) = mult(mult(iPr_def_11,iPr_def_10),X0),
inference(superposition,[status(thm)],[c_84,c_86]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : rd(mult(X0,mult(X1,mult(X0,X2))),X2) = mult(mult(X0,X1),X0),
inference(superposition,[status(thm)],[c_86,c_87]) ).
tcf(c_151,plain,
mult(iPr_def_10,x1) = x1,
inference(superposition,[status(thm)],[c_83,c_88]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,X1),mult(X1,mult(rd(X0,X1),X2))) = mult(mult(X0,rd(X0,X1)),X2),
inference(superposition,[status(thm)],[c_88,c_86]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_88,c_89]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(mult(X0,X1),X0),mult(X0,mult(X1,mult(X0,X2)))) = X2,
inference(superposition,[status(thm)],[c_86,c_89]) ).
tcf(c_155,plain,
ld(iPr_def_10,iPr_def_11) = x0,
inference(superposition,[status(thm)],[c_84,c_89]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_90,c_87]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(X0,X1),mult(X0,X2))) = mult(mult(X1,X0),X2),
inference(superposition,[status(thm)],[c_90,c_86]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(X1,mult(X0,ld(mult(mult(X0,X1),X0),X2)))) = X2,
inference(superposition,[status(thm)],[c_90,c_86]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(mult(mult(X0,mult(X1,mult(X0,X2))),mult(mult(X0,X1),X0)),X3) = mult(X0,mult(X1,mult(X0,mult(X2,mult(X0,mult(X1,mult(X0,X3))))))),
inference(demodulation,[status(thm)],[c_145,c_86]) ).
tcf(c_163,plain,
rd(x1,x1) = iPr_def_10,
inference(superposition,[status(thm)],[c_151,c_87]) ).
tcf(c_165,plain,
mult(iPr_def_10,x0) = iPr_def_11,
inference(superposition,[status(thm)],[c_155,c_90]) ).
tcf(c_168,plain,
ld(iPr_def_10,x1) = x1,
inference(superposition,[status(thm)],[c_83,c_153]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,rd(X1,mult(X0,X2))),X0) = rd(mult(X0,X1),X2),
inference(superposition,[status(thm)],[c_88,c_149]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] : rd(mult(X0,mult(X1,X2)),ld(X0,X2)) = mult(mult(X0,X1),X0),
inference(superposition,[status(thm)],[c_90,c_149]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] : rd(mult(iPr_def_10,mult(X0,mult(mult(iPr_def_11,iPr_def_10),X1))),mult(x0,mult(iPr_def_10,X1))) = mult(mult(iPr_def_10,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_148,c_149]) ).
tcf(c_195,plain,
! [X0: $i] : rd(mult(iPr_def_10,mult(X0,x1)),x1) = mult(mult(iPr_def_10,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_151,c_149]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(mult(X0,X1),X0),mult(X0,mult(X1,X2))) = ld(X0,X2),
inference(superposition,[status(thm)],[c_90,c_154]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),ld(X1,X2)) = mult(X1,mult(ld(X1,X0),X2)),
inference(superposition,[status(thm)],[c_90,c_158]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,X1),mult(ld(rd(X0,X1),X2),X0)) = mult(mult(X2,rd(X0,X1)),X1),
inference(superposition,[status(thm)],[c_88,c_158]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] : ld(X0,mult(mult(X1,X0),X2)) = mult(ld(X0,X1),mult(X0,X2)),
inference(superposition,[status(thm)],[c_158,c_89]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i,X2: $i] : rd(mult(mult(X0,X1),X2),mult(ld(X1,X0),mult(X1,X2))) = X1,
inference(superposition,[status(thm)],[c_158,c_87]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(X1,ld(mult(mult(X1,X0),X1),X2))) = ld(X1,X2),
inference(superposition,[status(thm)],[c_159,c_89]) ).
tcf(c_286,plain,
! [X0: $i] : mult(mult(iPr_def_11,iPr_def_10),mult(x0,ld(mult(mult(x0,iPr_def_10),x0),X0))) = mult(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_159,c_148]) ).
tcf(c_307,plain,
! [X0: $i] : mult(iPr_def_10,mult(x1,mult(iPr_def_10,X0))) = mult(mult(x1,iPr_def_10),X0),
inference(superposition,[status(thm)],[c_83,c_152]) ).
tcf(c_985,plain,
mult(mult(iPr_def_10,iPr_def_10),iPr_def_10) = rd(x1,x1),
inference(superposition,[status(thm)],[c_151,c_195]) ).
tcf(c_1078,plain,
! [X0: $i] : mult(mult(iPr_def_10,rd(X0,x1)),iPr_def_10) = rd(mult(iPr_def_10,X0),x1),
inference(superposition,[status(thm)],[c_151,c_187]) ).
tcf(c_1090,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(X0,rd(X1,mult(X0,X2))),rd(mult(X0,X1),X2)) = X0,
inference(superposition,[status(thm)],[c_187,c_89]) ).
tcf(c_1091,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,rd(X1,mult(X0,X2))) = rd(rd(mult(X0,X1),X2),X0),
inference(superposition,[status(thm)],[c_187,c_87]) ).
tcf(c_1119,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,rd(X1,X2)),X0) = rd(mult(X0,X1),ld(X0,X2)),
inference(superposition,[status(thm)],[c_88,c_190]) ).
tcf(c_1212,plain,
! [X0: $i] : mult(x1,mult(ld(x1,iPr_def_10),X0)) = mult(x1,ld(x1,X0)),
inference(superposition,[status(thm)],[c_151,c_230]) ).
tcf(c_1269,plain,
! [X0: $i] : mult(ld(x1,iPr_def_10),mult(x1,X0)) = ld(x1,mult(x1,X0)),
inference(superposition,[status(thm)],[c_151,c_238]) ).
tcf(c_1318,plain,
! [X0: $i] : rd(mult(mult(x1,iPr_def_10),X0),mult(x1,mult(iPr_def_10,X0))) = iPr_def_10,
inference(superposition,[status(thm)],[c_168,c_239]) ).
tcf(c_1367,plain,
! [X0: $i] : mult(x1,mult(iPr_def_10,ld(mult(x1,iPr_def_10),X0))) = ld(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_151,c_275]) ).
tcf(c_1384,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(mult(mult(X0,X1),X0),X2)) = ld(X1,ld(X0,X2)),
inference(superposition,[status(thm)],[c_275,c_89]) ).
tcf(c_1555,plain,
! [X0: $i] : mult(x0,ld(mult(mult(x0,iPr_def_10),x0),X0)) = ld(mult(iPr_def_11,iPr_def_10),mult(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_286,c_89]) ).
tcf(c_1617,plain,
mult(mult(iPr_def_10,iPr_def_10),iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_985,c_163]) ).
tcf(c_1620,plain,
! [X0: $i] : mult(ld(x1,iPr_def_10),mult(x1,X0)) = X0,
inference(demodulation,[status(thm)],[c_1269,c_89]) ).
tcf(c_1621,plain,
! [X0: $i] : mult(x1,mult(ld(x1,iPr_def_10),X0)) = X0,
inference(demodulation,[status(thm)],[c_1212,c_90]) ).
tcf(c_1643,plain,
! [X0: $i] : ld(mult(iPr_def_11,iPr_def_10),mult(iPr_def_10,X0)) = ld(iPr_def_10,ld(x0,X0)),
inference(demodulation,[status(thm)],[c_1555,c_1384]) ).
tcf(c_1917,plain,
! [X0: $i] : ld(iPr_def_10,mult(iPr_def_10,mult(iPr_def_10,X0))) = ld(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_1617,c_211]) ).
tcf(c_1937,plain,
! [X0: $i] : rd(X0,mult(x1,X0)) = ld(x1,iPr_def_10),
inference(superposition,[status(thm)],[c_1620,c_87]) ).
tcf(c_1977,plain,
! [X0: $i] : mult(ld(x1,iPr_def_10),X0) = ld(x1,X0),
inference(superposition,[status(thm)],[c_1621,c_89]) ).
tcf(c_2185,plain,
! [X0: $i] : mult(mult(iPr_def_10,mult(mult(iPr_def_10,X0),iPr_def_10)),iPr_def_10) = rd(mult(iPr_def_10,mult(iPr_def_10,mult(X0,x1))),x1),
inference(superposition,[status(thm)],[c_195,c_1078]) ).
tcf(c_2346,plain,
! [X0: $i] : rd(X0,mult(x1,mult(iPr_def_10,ld(mult(x1,iPr_def_10),X0)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_90,c_1318]) ).
tcf(c_2497,plain,
! [X0: $i] : mult(iPr_def_10,ld(mult(x1,iPr_def_10),X0)) = ld(x1,ld(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_1367,c_89]) ).
tcf(c_2510,plain,
! [X0: $i] : mult(mult(x1,iPr_def_10),ld(mult(x1,iPr_def_10),X0)) = mult(iPr_def_10,ld(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_1367,c_307]) ).
tcf(c_2525,plain,
ld(mult(iPr_def_11,iPr_def_10),x1) = ld(iPr_def_10,ld(x0,x1)),
inference(superposition,[status(thm)],[c_151,c_1643]) ).
tcf(c_2640,plain,
! [X0: $i,X1: $i] : mult(X0,rd(X1,mult(X0,X1))) = rd(X0,X0),
inference(superposition,[status(thm)],[c_87,c_1091]) ).
tcf(c_2740,plain,
! [X0: $i] : mult(mult(iPr_def_10,rd(x0,X0)),iPr_def_10) = rd(iPr_def_11,ld(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_165,c_1119]) ).
tcf(c_2801,plain,
! [X0: $i] : ld(iPr_def_10,X0) = mult(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_1917,c_89]) ).
tcf(c_2803,plain,
! [X0: $i] : mult(mult(iPr_def_10,rd(x0,X0)),iPr_def_10) = rd(iPr_def_11,mult(iPr_def_10,X0)),
inference(demodulation,[status(thm)],[c_2740,c_2801]) ).
tcf(c_2809,plain,
! [X0: $i] : mult(iPr_def_10,ld(mult(x1,iPr_def_10),X0)) = ld(x1,mult(iPr_def_10,X0)),
inference(demodulation,[status(thm)],[c_2497,c_2801]) ).
tcf(c_2835,plain,
! [X0: $i] : rd(X0,mult(x1,ld(x1,mult(iPr_def_10,X0)))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2346,c_2809]) ).
tcf(c_2836,plain,
! [X0: $i] : rd(X0,mult(iPr_def_10,X0)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2835,c_90]) ).
tcf(c_2865,plain,
! [X0: $i] : mult(mult(x1,iPr_def_10),ld(mult(x1,iPr_def_10),X0)) = mult(iPr_def_10,mult(iPr_def_10,X0)),
inference(demodulation,[status(thm)],[c_2510,c_2801]) ).
tcf(c_2866,plain,
! [X0: $i] : mult(iPr_def_10,mult(iPr_def_10,X0)) = X0,
inference(demodulation,[status(thm)],[c_2865,c_90]) ).
tcf(c_2953,plain,
! [X0: $i] : mult(mult(iPr_def_10,mult(mult(iPr_def_10,X0),iPr_def_10)),iPr_def_10) = rd(mult(X0,x1),x1),
inference(demodulation,[status(thm)],[c_2185,c_2866]) ).
tcf(c_2954,plain,
! [X0: $i] : mult(mult(iPr_def_10,mult(mult(iPr_def_10,X0),iPr_def_10)),iPr_def_10) = X0,
inference(demodulation,[status(thm)],[c_2953,c_87]) ).
tcf(c_3209,plain,
! [X0: $i] : ld(mult(iPr_def_11,iPr_def_10),mult(iPr_def_10,X0)) = mult(iPr_def_10,ld(x0,X0)),
inference(demodulation,[status(thm)],[c_1643,c_2801]) ).
tcf(c_4060,plain,
mult(iPr_def_10,iPr_def_11) = x0,
inference(superposition,[status(thm)],[c_165,c_2866]) ).
tcf(c_4062,plain,
! [X0: $i] : mult(iPr_def_10,mult(mult(iPr_def_11,iPr_def_10),X0)) = mult(x0,mult(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_148,c_2866]) ).
tcf(c_4063,plain,
! [X0: $i,X1: $i] : mult(ld(iPr_def_10,X0),mult(iPr_def_10,X1)) = mult(iPr_def_10,mult(mult(X0,iPr_def_10),X1)),
inference(superposition,[status(thm)],[c_158,c_2866]) ).
tcf(c_4090,plain,
! [X0: $i,X1: $i] : mult(mult(iPr_def_10,X0),mult(iPr_def_10,mult(mult(iPr_def_10,X0),X1))) = mult(mult(iPr_def_10,mult(X0,X0)),X1),
inference(superposition,[status(thm)],[c_2866,c_147]) ).
tcf(c_4153,plain,
! [X0: $i] : rd(ld(x1,X0),X0) = ld(x1,iPr_def_10),
inference(superposition,[status(thm)],[c_1977,c_87]) ).
tcf(c_4354,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(rd(X0,X0),X0),mult(X0,mult(rd(X1,mult(X0,X1)),X2))) = ld(X0,X2),
inference(superposition,[status(thm)],[c_2640,c_211]) ).
tcf(c_4358,plain,
! [X0: $i,X1: $i] : ld(X0,rd(X0,X0)) = rd(X1,mult(X0,X1)),
inference(superposition,[status(thm)],[c_2640,c_89]) ).
tcf(c_4365,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(mult(X0,X1),X0),mult(X0,mult(X1,rd(X0,X0)))) = rd(X2,mult(X0,X2)),
inference(superposition,[status(thm)],[c_2640,c_154]) ).
tcf(c_4457,plain,
! [X0: $i] : mult(mult(iPr_def_10,mult(X0,iPr_def_10)),iPr_def_10) = mult(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_2866,c_2954]) ).
tcf(c_4470,plain,
! [X0: $i] : mult(iPr_def_10,mult(mult(iPr_def_10,X0),iPr_def_10)) = rd(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_2954,c_87]) ).
tcf(c_4676,plain,
! [X0: $i,X1: $i] : mult(mult(iPr_def_10,X0),mult(iPr_def_10,X1)) = mult(iPr_def_10,mult(mult(X0,iPr_def_10),X1)),
inference(demodulation,[status(thm)],[c_4063,c_2801]) ).
tcf(c_4716,plain,
! [X0: $i,X1: $i] : rd(X0,mult(X1,X0)) = iPr_def_12(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_4365]) ).
tcf(c_4724,plain,
! [X0: $i,X1: $i] : ld(mult(rd(X0,X0),X0),mult(X0,mult(iPr_def_12(X0),X1))) = ld(X0,X1),
inference(demodulation,[status(thm)],[c_4354,c_4716]) ).
tcf(c_4725,plain,
! [X0: $i,X1: $i] : mult(iPr_def_12(X0),X1) = ld(X0,X1),
inference(demodulation,[status(thm)],[c_4724,c_89,c_88]) ).
tcf(c_4977,plain,
ld(x1,iPr_def_10) = iPr_def_12(x1),
inference(demodulation,[status(thm)],[c_1937,c_4716]) ).
tcf(c_4978,plain,
! [X0: $i] : mult(X0,iPr_def_12(X0)) = rd(X0,X0),
inference(demodulation,[status(thm)],[c_2640,c_4716]) ).
tcf(c_5015,plain,
mult(mult(iPr_def_11,iPr_def_10),iPr_def_11) = mult(iPr_def_10,mult(x0,x0)),
inference(superposition,[status(thm)],[c_4060,c_148]) ).
tcf(c_5091,plain,
! [X0: $i,X1: $i] : rd(ld(X0,X1),X1) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_4725,c_87]) ).
tcf(c_5110,plain,
! [X0: $i,X1: $i] : rd(X0,ld(X1,X0)) = iPr_def_12(iPr_def_12(X1)),
inference(superposition,[status(thm)],[c_4725,c_4716]) ).
tcf(c_5127,plain,
! [X0: $i] : rd(mult(iPr_def_10,ld(X0,x1)),x1) = mult(mult(iPr_def_10,iPr_def_12(X0)),iPr_def_10),
inference(superposition,[status(thm)],[c_4725,c_195]) ).
tcf(c_5182,plain,
! [X0: $i] : ld(X0,iPr_def_12(iPr_def_12(X0))) = rd(iPr_def_12(X0),iPr_def_12(X0)),
inference(superposition,[status(thm)],[c_4978,c_4725]) ).
tcf(c_5199,plain,
rd(iPr_def_12(x1),iPr_def_10) = iPr_def_12(x1),
inference(superposition,[status(thm)],[c_4977,c_4153]) ).
tcf(c_5522,plain,
! [X0: $i] : ld(X0,rd(X0,X0)) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_4358,c_4716]) ).
tcf(c_5663,plain,
! [X0: $i] : mult(iPr_def_10,mult(X0,iPr_def_10)) = rd(mult(iPr_def_10,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_2866,c_4470]) ).
tcf(c_5692,plain,
! [X0: $i] : mult(mult(iPr_def_10,X0),iPr_def_10) = mult(iPr_def_10,rd(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_4470,c_2866]) ).
tcf(c_5709,plain,
! [X0: $i] : ld(mult(mult(iPr_def_10,mult(iPr_def_10,X0)),iPr_def_10),rd(X0,iPr_def_10)) = ld(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_4470,c_211]) ).
tcf(c_5710,plain,
! [X0: $i] : mult(mult(iPr_def_10,mult(iPr_def_10,X0)),iPr_def_10) = rd(rd(X0,iPr_def_10),ld(iPr_def_10,iPr_def_10)),
inference(superposition,[status(thm)],[c_4470,c_190]) ).
tcf(c_5733,plain,
! [X0: $i] : iPr_def_12(iPr_def_12(X0)) = X0,
inference(demodulation,[status(thm)],[c_5110,c_157]) ).
tcf(c_5754,plain,
! [X0: $i] : rd(iPr_def_12(X0),iPr_def_12(X0)) = ld(X0,X0),
inference(demodulation,[status(thm)],[c_5182,c_5733]) ).
tcf(c_5798,plain,
! [X0: $i] : rd(mult(iPr_def_10,ld(X0,x1)),x1) = mult(iPr_def_10,rd(iPr_def_12(X0),iPr_def_10)),
inference(demodulation,[status(thm)],[c_5127,c_5692]) ).
tcf(c_5805,plain,
! [X0: $i] : mult(iPr_def_10,mult(iPr_def_10,mult(X0,iPr_def_10))) = rd(rd(X0,iPr_def_10),ld(iPr_def_10,iPr_def_10)),
inference(demodulation,[status(thm)],[c_5710,c_5692,c_5663]) ).
tcf(c_5806,plain,
! [X0: $i] : rd(rd(X0,iPr_def_10),mult(iPr_def_10,iPr_def_10)) = mult(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_5805,c_2801,c_2866]) ).
tcf(c_5807,plain,
! [X0: $i] : ld(mult(iPr_def_10,mult(iPr_def_10,mult(X0,iPr_def_10))),rd(X0,iPr_def_10)) = ld(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_5709,c_5692,c_5663]) ).
tcf(c_5808,plain,
! [X0: $i] : ld(mult(X0,iPr_def_10),rd(X0,iPr_def_10)) = mult(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_5807,c_2801,c_2866]) ).
tcf(c_6197,plain,
! [X0: $i,X1: $i] : ld(mult(iPr_def_10,rd(mult(X0,mult(mult(iPr_def_11,iPr_def_10),X1)),mult(iPr_def_10,mult(x0,mult(iPr_def_10,X1))))),mult(mult(iPr_def_10,X0),iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_194,c_1090]) ).
tcf(c_6234,plain,
ld(iPr_def_12(x1),iPr_def_12(x1)) = iPr_def_10,
inference(superposition,[status(thm)],[c_5199,c_153]) ).
tcf(c_6308,plain,
rd(ld(iPr_def_10,ld(x0,x1)),x1) = iPr_def_12(mult(iPr_def_11,iPr_def_10)),
inference(superposition,[status(thm)],[c_2525,c_5091]) ).
tcf(c_6611,plain,
! [X0: $i] : mult(ld(X0,X0),iPr_def_12(X0)) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_5754,c_88]) ).
tcf(c_6862,plain,
mult(iPr_def_10,rd(iPr_def_12(x0),iPr_def_10)) = iPr_def_12(mult(iPr_def_11,iPr_def_10)),
inference(demodulation,[status(thm)],[c_6308,c_2801,c_5798]) ).
tcf(c_7080,plain,
! [X0: $i] : ld(mult(iPr_def_10,X0),mult(iPr_def_10,rd(X0,iPr_def_10))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_6197,c_87,c_148,c_5692]) ).
tcf(c_7364,plain,
rd(iPr_def_11,mult(iPr_def_10,mult(x0,x0))) = iPr_def_12(mult(iPr_def_11,iPr_def_10)),
inference(superposition,[status(thm)],[c_5015,c_4716]) ).
tcf(c_7527,plain,
! [X0: $i] : mult(mult(X0,iPr_def_10),iPr_def_10) = rd(X0,mult(iPr_def_10,iPr_def_10)),
inference(superposition,[status(thm)],[c_87,c_5806]) ).
tcf(c_7568,plain,
ld(mult(iPr_def_12(x1),iPr_def_10),iPr_def_12(x1)) = mult(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_5199,c_5808]) ).
tcf(c_7855,plain,
ld(ld(x1,iPr_def_10),iPr_def_12(x1)) = mult(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_7568,c_4725]) ).
tcf(c_7856,plain,
mult(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_7855,c_4977,c_6234]) ).
tcf(c_8772,plain,
mult(iPr_def_10,mult(rd(iPr_def_12(x0),iPr_def_10),iPr_def_10)) = rd(iPr_def_12(mult(iPr_def_11,iPr_def_10)),iPr_def_10),
inference(superposition,[status(thm)],[c_6862,c_5663]) ).
tcf(c_8924,plain,
! [X0: $i] : mult(mult(X0,iPr_def_10),iPr_def_10) = rd(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_7856,c_7527]) ).
tcf(c_9380,plain,
rd(iPr_def_12(mult(iPr_def_11,iPr_def_10)),iPr_def_10) = mult(iPr_def_10,iPr_def_12(x0)),
inference(demodulation,[status(thm)],[c_8772,c_88]) ).
tcf(c_11542,plain,
mult(iPr_def_12(mult(iPr_def_11,iPr_def_10)),mult(iPr_def_10,mult(x0,x0))) = iPr_def_11,
inference(superposition,[status(thm)],[c_7364,c_88]) ).
tcf(c_24277,plain,
! [X0: $i] : mult(iPr_def_10,mult(iPr_def_12(mult(iPr_def_11,iPr_def_10)),mult(iPr_def_10,mult(mult(x0,x0),mult(iPr_def_10,mult(iPr_def_12(mult(iPr_def_11,iPr_def_10)),mult(iPr_def_10,X0))))))) = mult(mult(mult(iPr_def_10,iPr_def_11),mult(mult(iPr_def_10,iPr_def_12(mult(iPr_def_11,iPr_def_10))),iPr_def_10)),X0),
inference(superposition,[status(thm)],[c_11542,c_160]) ).
tcf(c_24731,plain,
! [X0: $i] : mult(mult(x0,mult(iPr_def_10,rd(iPr_def_12(mult(iPr_def_11,iPr_def_10)),iPr_def_10))),X0) = mult(ld(x0,x0),X0),
inference(demodulation,[status(thm)],[c_24277,c_90,c_238,c_2866,c_3209,c_4062,c_4676,c_4725,c_5692]) ).
tcf(c_24732,plain,
! [X0: $i] : mult(mult(x0,mult(iPr_def_10,mult(iPr_def_10,iPr_def_12(x0)))),X0) = mult(ld(x0,x0),X0),
inference(light_normalisation,[status(thm)],[c_24731,c_9380]) ).
tcf(c_24733,plain,
! [X0: $i] : mult(ld(x0,x0),X0) = mult(rd(x0,x0),X0),
inference(demodulation,[status(thm)],[c_24732,c_2866,c_4978]) ).
tcf(c_25299,plain,
! [X0: $i] : rd(mult(rd(x0,x0),X0),X0) = ld(x0,x0),
inference(superposition,[status(thm)],[c_24733,c_87]) ).
tcf(c_25342,plain,
mult(mult(rd(x0,x0),iPr_def_10),iPr_def_10) = rd(ld(x0,x0),iPr_def_10),
inference(superposition,[status(thm)],[c_24733,c_8924]) ).
tcf(c_25345,plain,
mult(mult(iPr_def_10,mult(rd(x0,x0),iPr_def_10)),iPr_def_10) = mult(iPr_def_10,ld(x0,x0)),
inference(superposition,[status(thm)],[c_24733,c_4457]) ).
tcf(c_25351,plain,
mult(rd(x0,x0),iPr_def_12(x0)) = iPr_def_12(x0),
inference(superposition,[status(thm)],[c_24733,c_6611]) ).
tcf(c_25469,plain,
ld(x0,x0) = rd(x0,x0),
inference(demodulation,[status(thm)],[c_25299,c_87]) ).
tcf(c_25512,plain,
rd(ld(x0,x0),iPr_def_10) = rd(rd(x0,x0),iPr_def_10),
inference(demodulation,[status(thm)],[c_25342,c_8924]) ).
tcf(c_25562,plain,
mult(iPr_def_10,ld(x0,x0)) = mult(iPr_def_10,rd(x0,x0)),
inference(demodulation,[status(thm)],[c_25345,c_4457]) ).
tcf(c_26538,plain,
ld(rd(x0,x0),iPr_def_12(x0)) = iPr_def_12(x0),
inference(superposition,[status(thm)],[c_25351,c_89]) ).
tcf(c_26931,plain,
mult(mult(iPr_def_10,rd(x0,x0)),iPr_def_10) = mult(iPr_def_10,rd(ld(x0,x0),iPr_def_10)),
inference(superposition,[status(thm)],[c_25562,c_5692]) ).
tcf(c_27419,plain,
mult(iPr_def_10,rd(ld(x0,x0),iPr_def_10)) = rd(iPr_def_11,mult(iPr_def_10,x0)),
inference(demodulation,[status(thm)],[c_26931,c_2803]) ).
tcf(c_27420,plain,
mult(iPr_def_10,rd(rd(x0,x0),iPr_def_10)) = rd(iPr_def_11,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_27419,c_165,c_25512]) ).
tcf(c_28328,plain,
mult(mult(iPr_def_12(x0),rd(x0,x0)),x0) = mult(rd(x0,x0),mult(iPr_def_12(x0),x0)),
inference(superposition,[status(thm)],[c_26538,c_231]) ).
tcf(c_28554,plain,
mult(iPr_def_10,mult(rd(rd(x0,x0),iPr_def_10),iPr_def_10)) = rd(rd(iPr_def_11,iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_27420,c_5663]) ).
tcf(c_28574,plain,
ld(mult(iPr_def_10,rd(x0,x0)),rd(iPr_def_11,iPr_def_11)) = iPr_def_10,
inference(superposition,[status(thm)],[c_27420,c_7080]) ).
tcf(c_29412,plain,
mult(iPr_def_10,rd(x0,x0)) = rd(rd(iPr_def_11,iPr_def_11),iPr_def_10),
inference(demodulation,[status(thm)],[c_28554,c_88]) ).
tcf(c_29472,plain,
mult(rd(x0,x0),ld(x0,x0)) = ld(x0,x0),
inference(demodulation,[status(thm)],[c_28328,c_4725,c_5522]) ).
tcf(c_29473,plain,
mult(rd(x0,x0),rd(x0,x0)) = rd(x0,x0),
inference(light_normalisation,[status(thm)],[c_29472,c_25469]) ).
tcf(c_30119,plain,
! [X0: $i] : rd(mult(mult(rd(iPr_def_11,iPr_def_11),mult(iPr_def_10,rd(x0,x0))),X0),mult(iPr_def_10,mult(mult(iPr_def_10,rd(x0,x0)),X0))) = mult(iPr_def_10,rd(x0,x0)),
inference(superposition,[status(thm)],[c_28574,c_239]) ).
tcf(c_30129,plain,
! [X0: $i] : mult(mult(iPr_def_10,rd(x0,x0)),mult(iPr_def_10,mult(mult(iPr_def_10,rd(x0,x0)),X0))) = mult(mult(rd(iPr_def_11,iPr_def_11),mult(iPr_def_10,rd(x0,x0))),X0),
inference(superposition,[status(thm)],[c_29412,c_152]) ).
tcf(c_30982,plain,
! [X0: $i] : mult(mult(rd(iPr_def_11,iPr_def_11),mult(iPr_def_10,rd(x0,x0))),X0) = mult(mult(iPr_def_10,mult(rd(x0,x0),rd(x0,x0))),X0),
inference(demodulation,[status(thm)],[c_30129,c_4090]) ).
tcf(c_30983,plain,
! [X0: $i] : mult(mult(rd(iPr_def_11,iPr_def_11),mult(iPr_def_10,rd(x0,x0))),X0) = mult(mult(iPr_def_10,rd(x0,x0)),X0),
inference(light_normalisation,[status(thm)],[c_30982,c_29473]) ).
tcf(c_30985,plain,
! [X0: $i] : rd(mult(mult(iPr_def_10,rd(x0,x0)),X0),mult(iPr_def_10,mult(mult(iPr_def_10,rd(x0,x0)),X0))) = mult(iPr_def_10,rd(x0,x0)),
inference(demodulation,[status(thm)],[c_30119,c_30983]) ).
tcf(c_30986,plain,
mult(iPr_def_10,rd(x0,x0)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_30985,c_2836]) ).
tcf(c_31638,plain,
mult(iPr_def_10,iPr_def_10) = rd(x0,x0),
inference(superposition,[status(thm)],[c_30986,c_2866]) ).
tcf(c_32333,plain,
rd(x0,x0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_31638,c_7856]) ).
tcf(c_33765,plain,
mult(iPr_def_10,x0) = x0,
inference(superposition,[status(thm)],[c_32333,c_88]) ).
tcf(c_34345,plain,
x0 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_33765,c_165]) ).
tcf(c_35094,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_85,c_34345]) ).
tcf(c_35095,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_35094]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP654-12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 15:32:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running UEQ theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 272.14/36.48 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 272.14/36.48 % SZS status Started for theBenchmark.p
% 272.14/36.48 % SZS status Unsatisfiable for theBenchmark.p
% 272.14/36.48
% 272.14/36.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 272.14/36.48
% 272.14/36.48 % ------ iProver source info
% 272.14/36.48
% 272.14/36.48 % git: date: 2026-07-19 20:42:38 +0200
% 272.14/36.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 272.14/36.48 % git: non_committed_changes: false
% 272.14/36.48
% 272.14/36.48 % ------ Parsing...% successful
% 272.14/36.48
% 272.14/36.48
% 272.14/36.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 272.14/36.48
% 272.14/36.48 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 272.14/36.48
% 272.14/36.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 272.14/36.48
% 272.14/36.48 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 272.14/36.48 % ------ Proving...
% 272.14/36.48 % ------ Problem Properties
% 272.14/36.48
% 272.14/36.48 %
% 272.14/36.48 % clauses 8
% 272.14/36.48 % conjectures 1
% 272.14/36.48 % EPR 1
% 272.14/36.48 % Horn 8
% 272.14/36.48 % unary 8
% 272.14/36.48 % binary 0
% 272.14/36.48 % lits 8
% 272.14/36.48 % lits eq 8
% 272.14/36.48 % fd_pure 0
% 272.14/36.48 % fd_pseudo 0
% 272.14/36.48 % fd_cond 0
% 272.14/36.48 % fd_pseudo_cond 0
% 272.14/36.48 % AC symbols 0
% 272.14/36.48
% 272.14/36.48 % ------ Input Options Time Limit: Unbounded
% 272.14/36.48
% 272.14/36.48
% 272.14/36.48 % ------
% 272.14/36.48 % Current options:
% 272.14/36.48 % ------
% 272.14/36.48
% 272.14/36.48
% 272.14/36.48 %
% 272.14/36.48
% 272.14/36.48 % ------ Proving...
% 272.14/36.48 %
% 272.14/36.48
% 272.14/36.48 % SZS status Unsatisfiable for theBenchmark.p
% 272.14/36.48
% 272.14/36.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 272.14/36.48
% 272.14/36.48
%------------------------------------------------------------------------------