%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP655-13 : 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 : n015.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 208.11s 39.47s
% Output : CNFRefutation 208.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 8
% Syntax : Number of formulae : 172 ( 172 unt; 2 def)
% Number of atoms : 578 ( 171 equ)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 198 ( 0 sgn 198 !; 0 ?; 187 :)
% 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(X2,X1))) = mult(mult(mult(X0,X1),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,negated_conjecture,
mult(x0,ld(x1,x1)) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f7,plain,
x0 != mult(x0,ld(x1,x1)),
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),X2),X1) = mult(X0,mult(X1,mult(X2,X1))),
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,negated_conjecture,
mult(x0,ld(x1,x1)) != x0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,definition,
iPr_def_10 = ld(x1,x1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_84,definition,
iPr_def_11 = mult(x0,iPr_def_10),
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),X2),X1) = mult(X0,mult(X1,mult(X2,X1))),
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_140,plain,
rd(iPr_def_11,iPr_def_10) = x0,
inference(superposition,[status(thm)],[c_84,c_87]) ).
tcf(c_141,plain,
mult(x0,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_140,c_88]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_88,c_89]) ).
tcf(c_147,plain,
mult(x1,iPr_def_10) = x1,
inference(superposition,[status(thm)],[c_83,c_90]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_90,c_87]) ).
tcf(c_151,plain,
ld(x1,x1) = iPr_def_10,
inference(superposition,[status(thm)],[c_147,c_89]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(X1,mult(ld(mult(X0,X1),X2),X1))) = mult(X2,X1),
inference(superposition,[status(thm)],[c_90,c_86]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(X0,X1),mult(X2,ld(X0,X1)))) = mult(mult(X1,X2),ld(X0,X1)),
inference(superposition,[status(thm)],[c_90,c_86]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,X1),mult(X1,mult(X2,X1))) = mult(mult(X0,X2),X1),
inference(superposition,[status(thm)],[c_88,c_86]) ).
tcf(c_169,plain,
! [X0: $i] : mult(x0,mult(iPr_def_10,mult(X0,iPr_def_10))) = mult(mult(iPr_def_11,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_141,c_86]) ).
tcf(c_171,plain,
! [X0: $i] : mult(x1,mult(iPr_def_10,mult(X0,iPr_def_10))) = mult(mult(x1,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_147,c_86]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(mult(X0,X1),X2),mult(X0,mult(X1,mult(X2,X1)))) = X1,
inference(superposition,[status(thm)],[c_86,c_89]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i] : rd(mult(X0,mult(X1,mult(X2,X1))),X1) = mult(mult(X0,X1),X2),
inference(superposition,[status(thm)],[c_86,c_87]) ).
tcf(c_185,plain,
! [X0: $i] : mult(mult(iPr_def_11,rd(X0,iPr_def_10)),iPr_def_10) = mult(x0,mult(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_88,c_169]) ).
tcf(c_191,plain,
! [X0: $i] : ld(x0,mult(mult(iPr_def_11,X0),iPr_def_10)) = mult(iPr_def_10,mult(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_169,c_89]) ).
tcf(c_192,plain,
! [X0: $i] : rd(mult(mult(iPr_def_11,X0),iPr_def_10),mult(iPr_def_10,mult(X0,iPr_def_10))) = x0,
inference(superposition,[status(thm)],[c_169,c_87]) ).
tcf(c_218,plain,
! [X0: $i] : mult(mult(x1,rd(X0,iPr_def_10)),iPr_def_10) = mult(x1,mult(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_88,c_171]) ).
tcf(c_226,plain,
! [X0: $i] : ld(x1,mult(mult(x1,X0),iPr_def_10)) = mult(iPr_def_10,mult(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_171,c_89]) ).
tcf(c_264,plain,
! [X0: $i] : rd(mult(x0,mult(iPr_def_10,X0)),iPr_def_10) = mult(iPr_def_11,rd(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_185,c_87]) ).
tcf(c_279,plain,
! [X0: $i] : mult(iPr_def_10,mult(ld(iPr_def_11,X0),iPr_def_10)) = ld(x0,mult(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_90,c_191]) ).
tcf(c_310,plain,
! [X0: $i] : rd(mult(x1,mult(iPr_def_10,X0)),iPr_def_10) = mult(x1,rd(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_218,c_87]) ).
tcf(c_328,plain,
mult(iPr_def_10,mult(iPr_def_10,iPr_def_10)) = ld(x1,x1),
inference(superposition,[status(thm)],[c_147,c_226]) ).
tcf(c_332,plain,
mult(iPr_def_10,mult(iPr_def_10,iPr_def_10)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_328,c_151]) ).
tcf(c_338,plain,
rd(mult(mult(iPr_def_11,iPr_def_10),iPr_def_10),iPr_def_10) = x0,
inference(superposition,[status(thm)],[c_332,c_192]) ).
tcf(c_342,plain,
mult(iPr_def_11,iPr_def_10) = x0,
inference(demodulation,[status(thm)],[c_338,c_87]) ).
tcf(c_345,plain,
! [X0: $i] : mult(iPr_def_11,mult(iPr_def_10,mult(X0,iPr_def_10))) = mult(mult(x0,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_342,c_86]) ).
tcf(c_449,plain,
! [X0: $i] : mult(iPr_def_11,rd(ld(iPr_def_10,X0),iPr_def_10)) = rd(mult(x0,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_90,c_264]) ).
tcf(c_461,plain,
! [X0: $i] : ld(iPr_def_10,ld(x0,mult(X0,iPr_def_10))) = mult(ld(iPr_def_11,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_279,c_89]) ).
tcf(c_493,plain,
! [X0: $i] : mult(x1,rd(ld(iPr_def_10,X0),iPr_def_10)) = rd(mult(x1,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_90,c_310]) ).
tcf(c_551,plain,
! [X0: $i] : ld(iPr_def_11,mult(mult(x0,X0),iPr_def_10)) = mult(iPr_def_10,mult(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_345,c_89]) ).
tcf(c_653,plain,
! [X0: $i] : ld(iPr_def_11,rd(mult(x0,X0),iPr_def_10)) = rd(ld(iPr_def_10,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_449,c_89]) ).
tcf(c_675,plain,
ld(iPr_def_10,ld(x0,x0)) = mult(ld(iPr_def_11,iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_342,c_461]) ).
tcf(c_728,plain,
mult(x1,rd(mult(ld(iPr_def_11,iPr_def_11),iPr_def_10),iPr_def_10)) = rd(mult(x1,ld(x0,x0)),iPr_def_10),
inference(superposition,[status(thm)],[c_675,c_493]) ).
tcf(c_736,plain,
rd(mult(x1,ld(x0,x0)),iPr_def_10) = mult(x1,ld(iPr_def_11,iPr_def_11)),
inference(demodulation,[status(thm)],[c_728,c_87]) ).
tcf(c_860,plain,
! [X0: $i] : mult(iPr_def_10,mult(ld(x0,X0),iPr_def_10)) = ld(iPr_def_11,mult(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_90,c_551]) ).
tcf(c_1016,plain,
ld(mult(x1,ld(iPr_def_11,iPr_def_11)),mult(x1,ld(x0,x0))) = iPr_def_10,
inference(superposition,[status(thm)],[c_736,c_143]) ).
tcf(c_1152,plain,
! [X0: $i] : ld(iPr_def_10,ld(iPr_def_11,mult(X0,iPr_def_10))) = mult(ld(x0,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_860,c_89]) ).
tcf(c_1305,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,X1),mult(X1,mult(ld(X0,X2),X1))) = mult(X2,X1),
inference(superposition,[status(thm)],[c_88,c_164]) ).
tcf(c_1338,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(mult(X1,X0),X2),X0)) = ld(X1,mult(X2,X0)),
inference(superposition,[status(thm)],[c_164,c_89]) ).
tcf(c_1569,plain,
! [X0: $i] : mult(mult(X0,iPr_def_10),iPr_def_10) = mult(rd(X0,iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_332,c_167]) ).
tcf(c_1572,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,rd(X1,X2)),X2) = mult(rd(X0,X2),mult(X2,X1)),
inference(superposition,[status(thm)],[c_88,c_167]) ).
tcf(c_1605,plain,
! [X0: $i,X1: $i,X2: $i] : ld(rd(X0,X1),mult(mult(X0,X2),X1)) = mult(X1,mult(X2,X1)),
inference(superposition,[status(thm)],[c_167,c_89]) ).
tcf(c_1608,plain,
! [X0: $i] : mult(mult(X0,iPr_def_10),iPr_def_10) = X0,
inference(demodulation,[status(thm)],[c_1569,c_88]) ).
tcf(c_1801,plain,
! [X0: $i,X1: $i] : mult(mult(X0,iPr_def_10),mult(iPr_def_10,mult(X1,iPr_def_10))) = mult(mult(X0,X1),iPr_def_10),
inference(superposition,[status(thm)],[c_1608,c_86]) ).
tcf(c_1802,plain,
! [X0: $i] : ld(mult(X0,iPr_def_10),X0) = iPr_def_10,
inference(superposition,[status(thm)],[c_1608,c_89]) ).
tcf(c_1803,plain,
! [X0: $i] : mult(X0,iPr_def_10) = rd(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_1608,c_87]) ).
tcf(c_1837,plain,
! [X0: $i] : ld(iPr_def_11,mult(mult(x0,X0),iPr_def_10)) = rd(ld(iPr_def_10,X0),iPr_def_10),
inference(demodulation,[status(thm)],[c_653,c_1803]) ).
tcf(c_1839,plain,
! [X0: $i] : mult(iPr_def_10,mult(X0,iPr_def_10)) = rd(ld(iPr_def_10,X0),iPr_def_10),
inference(demodulation,[status(thm)],[c_1837,c_551]) ).
tcf(c_2335,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_89,c_1839]) ).
tcf(c_2345,plain,
! [X0: $i] : mult(mult(iPr_def_10,mult(X0,iPr_def_10)),iPr_def_10) = ld(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_1839,c_88]) ).
tcf(c_2347,plain,
! [X0: $i] : mult(iPr_def_10,mult(mult(iPr_def_10,X0),iPr_def_10)) = mult(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_2335,c_1803]) ).
tcf(c_2834,plain,
ld(iPr_def_10,ld(iPr_def_11,iPr_def_11)) = mult(ld(x0,x0),iPr_def_10),
inference(superposition,[status(thm)],[c_141,c_1152]) ).
tcf(c_2892,plain,
rd(ld(iPr_def_11,iPr_def_11),mult(ld(x0,x0),iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_2834,c_149]) ).
tcf(c_4890,plain,
! [X0: $i,X1: $i,X2: $i] : ld(X0,mult(X1,mult(X2,mult(ld(mult(X1,X2),X0),X2)))) = X2,
inference(superposition,[status(thm)],[c_90,c_173]) ).
tcf(c_4993,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(mult(X0,X1),rd(X2,X1)),mult(X0,mult(X1,X2))) = X1,
inference(superposition,[status(thm)],[c_88,c_173]) ).
tcf(c_5240,plain,
! [X0: $i,X1: $i] : mult(mult(X0,iPr_def_10),mult(iPr_def_10,X1)) = rd(mult(X0,mult(X1,iPr_def_10)),iPr_def_10),
inference(superposition,[status(thm)],[c_2347,c_174]) ).
tcf(c_5242,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),rd(X2,X1)) = rd(mult(X0,mult(X1,X2)),X1),
inference(superposition,[status(thm)],[c_88,c_174]) ).
tcf(c_5305,plain,
! [X0: $i,X1: $i] : mult(mult(X0,mult(X1,iPr_def_10)),iPr_def_10) = mult(mult(X0,iPr_def_10),mult(iPr_def_10,X1)),
inference(demodulation,[status(thm)],[c_5240,c_1803]) ).
tcf(c_5347,plain,
! [X0: $i] : mult(mult(iPr_def_10,iPr_def_10),mult(iPr_def_10,X0)) = ld(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_2345,c_5305]) ).
tcf(c_5925,plain,
! [X0: $i] : rd(ld(iPr_def_10,X0),mult(iPr_def_10,X0)) = mult(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_5347,c_87]) ).
tcf(c_14811,plain,
! [X0: $i,X1: $i,X2: $i] : ld(rd(X0,X1),mult(X2,X1)) = mult(X1,mult(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_1305,c_89]) ).
tcf(c_15070,plain,
! [X0: $i,X1: $i,X2: $i] : ld(X0,ld(X1,mult(X2,X0))) = mult(ld(mult(X1,X0),X2),X0),
inference(superposition,[status(thm)],[c_1338,c_89]) ).
tcf(c_24271,plain,
! [X0: $i] : ld(mult(mult(X0,x0),rd(iPr_def_10,x0)),mult(X0,iPr_def_11)) = x0,
inference(superposition,[status(thm)],[c_141,c_4993]) ).
tcf(c_24273,plain,
! [X0: $i] : ld(mult(mult(X0,x1),rd(iPr_def_10,x1)),mult(X0,x1)) = x1,
inference(superposition,[status(thm)],[c_147,c_4993]) ).
tcf(c_26079,plain,
! [X0: $i] : ld(mult(X0,rd(iPr_def_10,x0)),mult(rd(X0,x0),iPr_def_11)) = x0,
inference(superposition,[status(thm)],[c_88,c_24271]) ).
tcf(c_26130,plain,
! [X0: $i] : ld(mult(X0,rd(iPr_def_10,x1)),X0) = x1,
inference(superposition,[status(thm)],[c_88,c_24273]) ).
tcf(c_26146,plain,
! [X0: $i] : ld(X0,rd(X0,rd(iPr_def_10,x1))) = x1,
inference(superposition,[status(thm)],[c_88,c_26130]) ).
tcf(c_26155,plain,
! [X0: $i] : mult(X0,rd(iPr_def_10,x1)) = rd(X0,x1),
inference(superposition,[status(thm)],[c_26130,c_149]) ).
tcf(c_26172,plain,
! [X0: $i] : rd(X0,rd(iPr_def_10,x1)) = mult(X0,x1),
inference(superposition,[status(thm)],[c_26146,c_90]) ).
tcf(c_26250,plain,
! [X0: $i] : ld(X0,rd(X0,x1)) = rd(iPr_def_10,x1),
inference(superposition,[status(thm)],[c_26155,c_89]) ).
tcf(c_26411,plain,
rd(rd(iPr_def_10,x1),mult(iPr_def_10,rd(iPr_def_10,x1))) = mult(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_26250,c_5925]) ).
tcf(c_26435,plain,
mult(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_26411,c_88,c_26155,c_26172]) ).
tcf(c_26481,plain,
! [X0: $i] : rd(ld(iPr_def_10,X0),mult(iPr_def_10,X0)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_5925,c_26435]) ).
tcf(c_26511,plain,
! [X0: $i] : ld(rd(iPr_def_10,X0),mult(iPr_def_10,X0)) = mult(X0,mult(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_26435,c_1605]) ).
tcf(c_26705,plain,
rd(mult(ld(x0,x0),iPr_def_10),mult(iPr_def_10,ld(iPr_def_11,iPr_def_11))) = iPr_def_10,
inference(superposition,[status(thm)],[c_2834,c_26481]) ).
tcf(c_28927,plain,
! [X0: $i] : ld(X0,mult(rd(rd(X0,rd(iPr_def_10,x0)),x0),iPr_def_11)) = x0,
inference(superposition,[status(thm)],[c_88,c_26079]) ).
tcf(c_31328,plain,
! [X0: $i] : ld(rd(iPr_def_10,ld(iPr_def_10,X0)),X0) = mult(ld(iPr_def_10,X0),X0),
inference(superposition,[status(thm)],[c_90,c_26511]) ).
tcf(c_31350,plain,
! [X0: $i] : rd(mult(iPr_def_10,X0),mult(X0,mult(iPr_def_10,X0))) = rd(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_26511,c_149]) ).
tcf(c_31518,plain,
! [X0: $i] : mult(rd(rd(X0,rd(iPr_def_10,x0)),x0),iPr_def_11) = mult(X0,x0),
inference(superposition,[status(thm)],[c_28927,c_90]) ).
tcf(c_31521,plain,
! [X0: $i] : rd(mult(rd(rd(X0,rd(iPr_def_10,x0)),x0),iPr_def_11),x0) = X0,
inference(superposition,[status(thm)],[c_28927,c_149]) ).
tcf(c_39046,plain,
! [X0: $i] : mult(rd(iPr_def_10,ld(iPr_def_10,X0)),mult(ld(iPr_def_10,X0),X0)) = X0,
inference(superposition,[status(thm)],[c_31328,c_90]) ).
tcf(c_41523,plain,
! [X0: $i] : rd(rd(X0,rd(iPr_def_10,x0)),x0) = rd(mult(X0,x0),iPr_def_11),
inference(superposition,[status(thm)],[c_31518,c_87]) ).
tcf(c_41553,plain,
! [X0: $i] : rd(mult(rd(mult(X0,x0),iPr_def_11),iPr_def_11),x0) = X0,
inference(light_normalisation,[status(thm)],[c_31521,c_41523]) ).
tcf(c_52932,plain,
! [X0: $i,X1: $i] : mult(X0,mult(ld(X1,rd(X1,X0)),X0)) = X0,
inference(superposition,[status(thm)],[c_14811,c_89]) ).
tcf(c_53439,plain,
! [X0: $i,X1: $i] : mult(ld(X0,rd(X0,X1)),X1) = ld(X1,X1),
inference(superposition,[status(thm)],[c_52932,c_89]) ).
tcf(c_53452,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),rd(mult(ld(X2,rd(X2,X1)),X1),X1)) = rd(mult(X0,X1),X1),
inference(superposition,[status(thm)],[c_52932,c_5242]) ).
tcf(c_53523,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),ld(X2,rd(X2,X1))) = X0,
inference(demodulation,[status(thm)],[c_53452,c_87]) ).
tcf(c_53835,plain,
! [X0: $i] : rd(mult(rd(ld(x0,x0),iPr_def_11),iPr_def_11),x0) = ld(X0,rd(X0,x0)),
inference(superposition,[status(thm)],[c_53439,c_41553]) ).
tcf(c_53884,plain,
! [X0: $i] : ld(X0,rd(X0,x0)) = rd(ld(x0,x0),x0),
inference(demodulation,[status(thm)],[c_53835,c_88]) ).
tcf(c_55035,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(X0,X1),X0) = ld(X2,rd(X2,X1)),
inference(superposition,[status(thm)],[c_53523,c_89]) ).
tcf(c_55058,plain,
! [X0: $i,X1: $i] : ld(mult(X0,X1),X0) = iPr_def_12(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_55035]) ).
tcf(c_55059,plain,
! [X0: $i,X1: $i] : ld(X0,rd(X0,X1)) = iPr_def_12(X1),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_55035]) ).
tcf(c_55088,plain,
iPr_def_12(iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1802,c_55058]) ).
tcf(c_55146,plain,
! [X0: $i] : mult(iPr_def_12(X0),X0) = ld(X0,X0),
inference(demodulation,[status(thm)],[c_53439,c_55059]) ).
tcf(c_55148,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),iPr_def_12(X1)) = X0,
inference(demodulation,[status(thm)],[c_53523,c_55059]) ).
tcf(c_55861,plain,
! [X0: $i,X1: $i] : iPr_def_12(ld(X0,X1)) = ld(X1,X0),
inference(superposition,[status(thm)],[c_90,c_55058]) ).
tcf(c_56014,plain,
! [X0: $i] : ld(X0,rd(iPr_def_10,ld(iPr_def_10,X0))) = iPr_def_12(mult(ld(iPr_def_10,X0),X0)),
inference(superposition,[status(thm)],[c_39046,c_55058]) ).
tcf(c_56029,plain,
! [X0: $i,X1: $i] : rd(X0,iPr_def_12(X1)) = mult(X0,X1),
inference(superposition,[status(thm)],[c_55058,c_149]) ).
tcf(c_56135,plain,
iPr_def_12(mult(ld(x0,x0),iPr_def_10)) = ld(ld(iPr_def_11,iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_2892,c_55059]) ).
tcf(c_56150,plain,
ld(mult(ld(x0,x0),iPr_def_10),iPr_def_10) = iPr_def_12(mult(iPr_def_10,ld(iPr_def_11,iPr_def_11))),
inference(superposition,[status(thm)],[c_26705,c_55059]) ).
tcf(c_56187,plain,
! [X0: $i] : ld(mult(iPr_def_10,X0),rd(iPr_def_10,X0)) = iPr_def_12(mult(X0,mult(iPr_def_10,X0))),
inference(superposition,[status(thm)],[c_31350,c_55059]) ).
tcf(c_56208,plain,
! [X0: $i,X1: $i] : mult(X0,iPr_def_12(X1)) = rd(X0,X1),
inference(superposition,[status(thm)],[c_55059,c_90]) ).
tcf(c_56961,plain,
! [X0: $i,X1: $i] : mult(X0,iPr_def_12(ld(X1,X0))) = X1,
inference(superposition,[status(thm)],[c_90,c_55148]) ).
tcf(c_57123,plain,
! [X0: $i] : mult(ld(X0,X0),iPr_def_12(X0)) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_55146,c_55148]) ).
tcf(c_57598,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X1,X2)) = rd(X0,ld(X2,X1)),
inference(superposition,[status(thm)],[c_55861,c_56029]) ).
tcf(c_57618,plain,
! [X0: $i] : ld(mult(iPr_def_10,ld(X0,iPr_def_10)),X0) = mult(ld(iPr_def_10,X0),X0),
inference(demodulation,[status(thm)],[c_31328,c_57598]) ).
tcf(c_58795,plain,
! [X0: $i] : mult(rd(X0,iPr_def_12(X0)),mult(iPr_def_12(X0),iPr_def_12(X0))) = mult(X0,iPr_def_12(X0)),
inference(superposition,[status(thm)],[c_57123,c_1305]) ).
tcf(c_58798,plain,
! [X0: $i] : mult(mult(X0,X0),rd(iPr_def_12(X0),X0)) = rd(X0,X0),
inference(demodulation,[status(thm)],[c_58795,c_56029,c_56208]) ).
tcf(c_70220,plain,
! [X0: $i] : mult(rd(mult(X0,X0),X0),mult(X0,iPr_def_12(X0))) = mult(rd(X0,X0),X0),
inference(superposition,[status(thm)],[c_58798,c_1572]) ).
tcf(c_70224,plain,
! [X0: $i] : mult(X0,rd(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_70220,c_88,c_87,c_56208]) ).
tcf(c_70288,plain,
! [X0: $i] : mult(iPr_def_12(X0),mult(iPr_def_12(X0),X0)) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_56029,c_70224]) ).
tcf(c_70296,plain,
! [X0: $i] : ld(X0,X0) = rd(X0,X0),
inference(superposition,[status(thm)],[c_70224,c_89]) ).
tcf(c_70343,plain,
mult(iPr_def_10,mult(rd(x0,x0),iPr_def_10)) = ld(iPr_def_11,mult(x0,iPr_def_10)),
inference(superposition,[status(thm)],[c_70224,c_551]) ).
tcf(c_70356,plain,
! [X0: $i] : mult(iPr_def_12(X0),ld(X0,X0)) = iPr_def_12(X0),
inference(demodulation,[status(thm)],[c_70288,c_55146]) ).
tcf(c_70357,plain,
mult(iPr_def_10,mult(rd(x0,x0),iPr_def_10)) = ld(iPr_def_11,iPr_def_11),
inference(demodulation,[status(thm)],[c_70343,c_141]) ).
tcf(c_70954,plain,
! [X0: $i] : mult(mult(X0,iPr_def_12(X0)),ld(X0,X0)) = mult(X0,mult(ld(X0,X0),iPr_def_12(X0))),
inference(superposition,[status(thm)],[c_70356,c_166]) ).
tcf(c_70960,plain,
! [X0: $i] : mult(ld(X0,X0),ld(X0,X0)) = ld(X0,X0),
inference(demodulation,[status(thm)],[c_70954,c_56208,c_57123,c_70296]) ).
tcf(c_79642,plain,
! [X0: $i] : mult(ld(iPr_def_10,rd(iPr_def_10,X0)),rd(iPr_def_10,X0)) = ld(mult(iPr_def_10,X0),rd(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_143,c_57618]) ).
tcf(c_79684,plain,
! [X0: $i] : ld(mult(iPr_def_10,X0),rd(iPr_def_10,X0)) = mult(iPr_def_12(X0),rd(iPr_def_10,X0)),
inference(demodulation,[status(thm)],[c_79642,c_55059]) ).
tcf(c_79685,plain,
! [X0: $i] : mult(iPr_def_12(X0),rd(iPr_def_10,X0)) = iPr_def_12(mult(X0,mult(iPr_def_10,X0))),
inference(light_normalisation,[status(thm)],[c_79684,c_56187]) ).
tcf(c_89540,plain,
iPr_def_12(mult(mult(ld(x0,x0),iPr_def_10),mult(iPr_def_10,mult(ld(x0,x0),iPr_def_10)))) = mult(ld(ld(iPr_def_11,iPr_def_11),iPr_def_10),rd(iPr_def_10,mult(ld(x0,x0),iPr_def_10))),
inference(superposition,[status(thm)],[c_56135,c_79685]) ).
tcf(c_89618,plain,
mult(ld(ld(iPr_def_11,iPr_def_11),iPr_def_10),rd(iPr_def_10,mult(ld(x0,x0),iPr_def_10))) = ld(ld(iPr_def_11,iPr_def_11),iPr_def_10),
inference(demodulation,[status(thm)],[c_89540,c_1801,c_56135,c_70960]) ).
tcf(c_107637,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(mult(mult(mult(X0,X1),X2),X1),X0),X1) = ld(X1,iPr_def_12(X2)),
inference(superposition,[status(thm)],[c_55058,c_15070]) ).
tcf(c_108105,plain,
! [X0: $i,X1: $i] : mult(iPr_def_12(mult(X0,mult(X1,X0))),X0) = ld(X0,iPr_def_12(X1)),
inference(demodulation,[status(thm)],[c_107637,c_86,c_55058]) ).
tcf(c_113651,plain,
! [X0: $i,X1: $i] : ld(iPr_def_12(mult(X0,mult(X1,X0))),ld(X0,iPr_def_12(X1))) = X0,
inference(superposition,[status(thm)],[c_108105,c_89]) ).
tcf(c_115768,plain,
! [X0: $i] : ld(iPr_def_12(mult(X0,mult(iPr_def_10,X0))),ld(X0,iPr_def_10)) = X0,
inference(superposition,[status(thm)],[c_55088,c_113651]) ).
tcf(c_116184,plain,
! [X0: $i] : mult(ld(X0,iPr_def_10),iPr_def_12(X0)) = iPr_def_12(mult(X0,mult(iPr_def_10,X0))),
inference(superposition,[status(thm)],[c_115768,c_56961]) ).
tcf(c_116192,plain,
! [X0: $i] : iPr_def_12(mult(X0,mult(iPr_def_10,X0))) = rd(ld(X0,iPr_def_10),X0),
inference(demodulation,[status(thm)],[c_116184,c_56208]) ).
tcf(c_116267,plain,
! [X0: $i] : mult(iPr_def_12(X0),rd(iPr_def_10,X0)) = rd(ld(X0,iPr_def_10),X0),
inference(demodulation,[status(thm)],[c_79685,c_116192]) ).
tcf(c_116317,plain,
rd(ld(mult(rd(x0,x0),iPr_def_10),iPr_def_10),mult(rd(x0,x0),iPr_def_10)) = iPr_def_12(mult(mult(rd(x0,x0),iPr_def_10),ld(iPr_def_11,iPr_def_11))),
inference(superposition,[status(thm)],[c_70357,c_116192]) ).
tcf(c_116376,plain,
rd(ld(mult(ld(x0,x0),iPr_def_10),iPr_def_10),mult(ld(x0,x0),iPr_def_10)) = iPr_def_12(mult(mult(ld(x0,x0),iPr_def_10),ld(iPr_def_11,iPr_def_11))),
inference(demodulation,[status(thm)],[c_116317,c_70296]) ).
tcf(c_116377,plain,
rd(iPr_def_12(mult(iPr_def_10,ld(iPr_def_11,iPr_def_11))),mult(ld(x0,x0),iPr_def_10)) = iPr_def_12(mult(mult(ld(x0,x0),iPr_def_10),ld(iPr_def_11,iPr_def_11))),
inference(light_normalisation,[status(thm)],[c_116376,c_56150]) ).
tcf(c_116694,plain,
mult(ld(ld(iPr_def_11,iPr_def_11),iPr_def_10),rd(iPr_def_10,mult(ld(x0,x0),iPr_def_10))) = rd(ld(mult(ld(x0,x0),iPr_def_10),iPr_def_10),mult(ld(x0,x0),iPr_def_10)),
inference(superposition,[status(thm)],[c_56135,c_116267]) ).
tcf(c_116793,plain,
iPr_def_12(mult(mult(ld(x0,x0),iPr_def_10),ld(iPr_def_11,iPr_def_11))) = ld(ld(iPr_def_11,iPr_def_11),iPr_def_10),
inference(light_normalisation,[status(thm)],[c_116694,c_56150,c_89618,c_116377]) ).
tcf(c_137415,plain,
! [X0: $i,X1: $i] : ld(mult(X0,mult(X1,mult(ld(mult(X0,X1),iPr_def_10),X1))),rd(iPr_def_10,X1)) = iPr_def_12(mult(X1,mult(X0,mult(X1,mult(ld(mult(X0,X1),iPr_def_10),X1))))),
inference(superposition,[status(thm)],[c_4890,c_56014]) ).
tcf(c_137578,plain,
! [X0: $i] : ld(mult(iPr_def_10,X0),rd(iPr_def_10,X0)) = rd(ld(X0,iPr_def_10),X0),
inference(demodulation,[status(thm)],[c_137415,c_90,c_1338,c_116192]) ).
tcf(c_137680,plain,
! [X0: $i] : mult(mult(iPr_def_10,X0),rd(ld(X0,iPr_def_10),X0)) = rd(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_137578,c_90]) ).
tcf(c_137799,plain,
mult(ld(iPr_def_11,iPr_def_11),rd(ld(mult(rd(x0,x0),iPr_def_10),iPr_def_10),mult(rd(x0,x0),iPr_def_10))) = rd(iPr_def_10,mult(rd(x0,x0),iPr_def_10)),
inference(superposition,[status(thm)],[c_70357,c_137680]) ).
tcf(c_137915,plain,
mult(ld(iPr_def_11,iPr_def_11),rd(ld(mult(ld(x0,x0),iPr_def_10),iPr_def_10),mult(ld(x0,x0),iPr_def_10))) = rd(iPr_def_10,mult(ld(x0,x0),iPr_def_10)),
inference(demodulation,[status(thm)],[c_137799,c_70296]) ).
tcf(c_137916,plain,
mult(ld(iPr_def_11,iPr_def_11),ld(ld(iPr_def_11,iPr_def_11),iPr_def_10)) = rd(iPr_def_10,mult(ld(x0,x0),iPr_def_10)),
inference(light_normalisation,[status(thm)],[c_137915,c_56150,c_116377,c_116793]) ).
tcf(c_137917,plain,
rd(iPr_def_10,mult(ld(x0,x0),iPr_def_10)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_137916,c_90]) ).
tcf(c_138012,plain,
mult(iPr_def_10,mult(ld(x0,x0),iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_137917,c_88]) ).
tcf(c_138030,plain,
ld(iPr_def_11,iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_138012,c_141,c_860]) ).
tcf(c_138103,plain,
ld(mult(x1,iPr_def_10),mult(x1,ld(x0,x0))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1016,c_138030]) ).
tcf(c_138106,plain,
ld(x0,x0) = iPr_def_10,
inference(demodulation,[status(thm)],[c_138103,c_89,c_147]) ).
tcf(c_138120,plain,
! [X0: $i] : ld(X0,rd(X0,x0)) = rd(iPr_def_10,x0),
inference(demodulation,[status(thm)],[c_53884,c_138106]) ).
tcf(c_138121,plain,
rd(iPr_def_10,x0) = iPr_def_12(x0),
inference(demodulation,[status(thm)],[c_138120,c_55059]) ).
tcf(c_138157,plain,
! [X0: $i] : ld(mult(X0,iPr_def_12(x0)),mult(rd(X0,x0),iPr_def_11)) = x0,
inference(demodulation,[status(thm)],[c_26079,c_138121]) ).
tcf(c_138159,plain,
x0 = iPr_def_11,
inference(demodulation,[status(thm)],[c_138157,c_89,c_56208]) ).
tcf(c_138672,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_85,c_138159]) ).
tcf(c_138673,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_138672]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP655-13 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/10.43 % Computer : n015.cluster.edu
% 0.16/10.43 % Model : x86_64 x86_64
% 0.16/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.43 % Memory : 8046.5625MB
% 0.16/10.43 % OS : Linux 6.8.0-71-generic
% 0.16/10.43 % CPULimit : 300
% 0.16/10.43 % WCLimit : 300
% 0.16/10.43 % DateTime : Wed Sep 23 15:34:21 UTC 2026
% 0.16/10.43 % CPUTime :
% 0.16/10.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/10.47 Running UEQ theorem proving
% 0.16/10.47 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
% 0.16/10.48
% 0.16/10.48 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.48
% 0.16/10.48 % Detected problem language: tptp
% 0.16/10.49 % Proving...
% 208.11/39.47 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 208.11/39.47 % SZS status Started for theBenchmark.p
% 208.11/39.47 % SZS status Unsatisfiable for theBenchmark.p
% 208.11/39.47
% 208.11/39.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 208.11/39.47
% 208.11/39.47 % ------ iProver source info
% 208.11/39.47
% 208.11/39.47 % git: date: 2026-07-19 20:42:38 +0200
% 208.11/39.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 208.11/39.47 % git: non_committed_changes: false
% 208.11/39.47
% 208.11/39.47 % ------ Parsing...% successful
% 208.11/39.47
% 208.11/39.47
% 208.11/39.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 208.11/39.47
% 208.11/39.47 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 208.11/39.47
% 208.11/39.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 208.11/39.47
% 208.11/39.47 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 208.11/39.47 % ------ Proving...
% 208.11/39.47 % ------ Problem Properties
% 208.11/39.47
% 208.11/39.47 %
% 208.11/39.47 % clauses 8
% 208.11/39.47 % conjectures 1
% 208.11/39.47 % EPR 1
% 208.11/39.47 % Horn 8
% 208.11/39.47 % unary 8
% 208.11/39.47 % binary 0
% 208.11/39.47 % lits 8
% 208.11/39.47 % lits eq 8
% 208.11/39.47 % fd_pure 0
% 208.11/39.47 % fd_pseudo 0
% 208.11/39.47 % fd_cond 0
% 208.11/39.47 % fd_pseudo_cond 0
% 208.11/39.47 % AC symbols 0
% 208.11/39.47
% 208.11/39.47 % ------ Input Options Time Limit: Unbounded
% 208.11/39.47
% 208.11/39.47
% 208.11/39.47 % ------
% 208.11/39.47 % Current options:
% 208.11/39.47 % ------
% 208.11/39.47
% 208.11/39.47
% 208.11/39.47 %
% 208.11/39.47
% 208.11/39.47 % ------ Proving...
% 208.11/39.47 %
% 208.11/39.47
% 208.11/39.47 % SZS status Unsatisfiable for theBenchmark.p
% 208.11/39.47
% 208.11/39.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 208.11/39.48
% 208.11/39.48
%------------------------------------------------------------------------------