%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP660+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 01:35:07 PM UTC 2026
% Result : Theorem 17.44s 5.29s
% Output : CNFRefutation 17.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 9
% Syntax : Number of formulae : 143 ( 135 unt; 3 def)
% Number of atoms : 519 ( 150 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 22 ( 14 ~; 6 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 101 !; 2 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X0,X1,X2] : mult(mult(mult(X2,X1),X0),X2) = mult(X2,mult(X1,mult(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f6,conjecture,
! [X0,X1] :
( mult(rd(X1,X1),X0) = X0
& mult(X0,rd(X1,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( mult(rd(X1,X1),X0) = X0
& mult(X0,rd(X1,X1)) = X0 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( mult(rd(X1,X1),X0) != X0
| mult(X0,rd(X1,X1)) != X0 ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
( sK0 != mult(rd(sK1,sK1),sK0)
| sK0 != mult(sK0,rd(sK1,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
fof(f10,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f14,plain,
! [X2,X0,X1] : mult(mult(mult(X2,X1),X0),X2) = mult(X2,mult(X1,mult(X0,X2))),
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
( sK0 != mult(rd(sK1,sK1),sK0)
| sK0 != mult(sK0,rd(sK1,sK1)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[],[f10]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[],[f11]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f13]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(mult(X0,X1),X2),X0) = mult(X0,mult(X1,mult(X2,X0))),
inference(cnf_transformation,[],[f14]) ).
tcf(c_54,negated_conjecture,
( ( mult(sK0,rd(sK1,sK1)) != sK0 )
| ( mult(rd(sK1,sK1),sK0) != sK0 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_81,definition,
iPr_def_10 = rd(sK1,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_82,definition,
iPr_def_11 = mult(iPr_def_10,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_83,definition,
iPr_def_12 = mult(sK0,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_84,negated_conjecture,
( ( iPr_def_12 != sK0 )
| ( iPr_def_11 != sK0 ) ),
inference(demodulation,[status(thm)],[c_54,c_83,c_81,c_82]) ).
tcf(c_140,plain,
ld(iPr_def_10,iPr_def_11) = sK0,
inference(superposition,[status(thm)],[c_82,c_50]) ).
tcf(c_141,plain,
ld(sK0,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_83,c_50]) ).
tcf(c_142,plain,
mult(iPr_def_10,sK0) = iPr_def_11,
inference(superposition,[status(thm)],[c_140,c_49]) ).
tcf(c_143,plain,
mult(sK0,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_141,c_49]) ).
tcf(c_145,plain,
mult(iPr_def_10,sK1) = sK1,
inference(superposition,[status(thm)],[c_81,c_51]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_51,c_50]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_49,c_52]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(X1,mult(ld(mult(X0,X1),X2),X0))) = mult(X2,X0),
inference(superposition,[status(thm)],[c_49,c_53]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(X0,X1),mult(X2,X0))) = mult(mult(X1,X2),X0),
inference(superposition,[status(thm)],[c_49,c_53]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] : rd(mult(X0,mult(X1,mult(X2,X0))),X0) = mult(mult(X0,X1),X2),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(mult(X0,X1),X2),mult(X0,mult(X1,mult(X2,X0)))) = X0,
inference(superposition,[status(thm)],[c_53,c_50]) ).
tcf(c_182,plain,
! [X0: $i] : mult(iPr_def_10,mult(sK1,mult(X0,iPr_def_10))) = mult(mult(sK1,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_145,c_53]) ).
tcf(c_184,plain,
ld(iPr_def_10,sK1) = sK1,
inference(superposition,[status(thm)],[c_145,c_50]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(mult(X1,X0),X2),X1)) = ld(X1,mult(X2,X1)),
inference(superposition,[status(thm)],[c_153,c_50]) ).
tcf(c_358,plain,
! [X0: $i] : rd(mult(mult(sK1,X0),iPr_def_10),mult(sK1,mult(X0,iPr_def_10))) = iPr_def_10,
inference(superposition,[status(thm)],[c_182,c_52]) ).
tcf(c_538,plain,
! [X0: $i] : mult(iPr_def_10,mult(ld(iPr_def_10,X0),iPr_def_12)) = mult(mult(X0,sK0),iPr_def_10),
inference(superposition,[status(thm)],[c_143,c_155]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i,X2: $i] : ld(X0,mult(mult(X1,X2),X0)) = mult(ld(X0,X1),mult(X2,X0)),
inference(superposition,[status(thm)],[c_155,c_50]) ).
tcf(c_632,plain,
! [X0: $i] : rd(mult(X0,iPr_def_10),mult(sK1,mult(ld(sK1,X0),iPr_def_10))) = iPr_def_10,
inference(superposition,[status(thm)],[c_49,c_358]) ).
tcf(c_978,plain,
! [X0: $i] : rd(mult(mult(X0,sK0),iPr_def_10),mult(ld(iPr_def_10,X0),iPr_def_12)) = iPr_def_10,
inference(superposition,[status(thm)],[c_538,c_52]) ).
tcf(c_1036,plain,
! [X0: $i] : mult(sK1,mult(ld(sK1,X0),iPr_def_10)) = ld(iPr_def_10,mult(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_632,c_146]) ).
tcf(c_1524,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,rd(X1,mult(X2,X0))),X2) = rd(mult(X0,X1),X0),
inference(superposition,[status(thm)],[c_51,c_162]) ).
tcf(c_1538,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),rd(X2,X0)) = rd(mult(X0,mult(X1,X2)),X0),
inference(superposition,[status(thm)],[c_51,c_162]) ).
tcf(c_1988,plain,
! [X0: $i] : ld(mult(mult(iPr_def_10,X0),sK0),mult(iPr_def_10,mult(X0,iPr_def_12))) = iPr_def_10,
inference(superposition,[status(thm)],[c_143,c_163]) ).
tcf(c_1990,plain,
! [X0: $i] : ld(mult(mult(sK1,X0),iPr_def_10),mult(sK1,mult(X0,sK1))) = sK1,
inference(superposition,[status(thm)],[c_145,c_163]) ).
tcf(c_2287,plain,
rd(mult(iPr_def_11,iPr_def_10),mult(ld(iPr_def_10,iPr_def_10),iPr_def_12)) = iPr_def_10,
inference(superposition,[status(thm)],[c_142,c_978]) ).
tcf(c_2342,plain,
ld(iPr_def_10,mult(iPr_def_11,iPr_def_10)) = mult(ld(iPr_def_10,iPr_def_10),iPr_def_12),
inference(superposition,[status(thm)],[c_2287,c_146]) ).
tcf(c_3104,plain,
! [X0: $i] : rd(ld(iPr_def_10,mult(X0,iPr_def_10)),mult(ld(sK1,X0),iPr_def_10)) = sK1,
inference(superposition,[status(thm)],[c_1036,c_52]) ).
tcf(c_3735,plain,
! [X0: $i] : ld(mult(mult(iPr_def_10,rd(X0,iPr_def_12)),sK0),mult(iPr_def_10,X0)) = iPr_def_10,
inference(superposition,[status(thm)],[c_51,c_1988]) ).
tcf(c_3758,plain,
ld(mult(mult(sK1,iPr_def_10),iPr_def_10),mult(sK1,sK1)) = sK1,
inference(superposition,[status(thm)],[c_145,c_1990]) ).
tcf(c_3773,plain,
mult(mult(sK1,iPr_def_10),iPr_def_10) = rd(mult(sK1,sK1),sK1),
inference(superposition,[status(thm)],[c_3758,c_148]) ).
tcf(c_3963,plain,
mult(mult(sK1,iPr_def_10),iPr_def_10) = sK1,
inference(demodulation,[status(thm)],[c_3773,c_52]) ).
tcf(c_3988,plain,
rd(sK1,mult(sK1,mult(iPr_def_10,iPr_def_10))) = iPr_def_10,
inference(superposition,[status(thm)],[c_3963,c_358]) ).
tcf(c_4067,plain,
mult(sK1,mult(iPr_def_10,iPr_def_10)) = ld(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_3988,c_146]) ).
tcf(c_4069,plain,
mult(sK1,mult(iPr_def_10,iPr_def_10)) = sK1,
inference(light_normalisation,[status(thm)],[c_4067,c_184]) ).
tcf(c_4077,plain,
ld(sK1,sK1) = mult(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_4069,c_50]) ).
tcf(c_4262,plain,
rd(iPr_def_10,mult(ld(sK1,iPr_def_10),iPr_def_10)) = sK1,
inference(superposition,[status(thm)],[c_50,c_3104]) ).
tcf(c_4310,plain,
mult(ld(sK1,iPr_def_10),iPr_def_10) = ld(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_4262,c_146]) ).
tcf(c_4332,plain,
rd(ld(sK1,iPr_def_10),iPr_def_10) = ld(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_4310,c_52]) ).
tcf(c_4333,plain,
ld(ld(sK1,iPr_def_10),ld(sK1,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_4310,c_50]) ).
tcf(c_4691,plain,
! [X0: $i] : mult(mult(iPr_def_10,rd(X0,iPr_def_12)),sK0) = rd(mult(iPr_def_10,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_3735,c_148]) ).
tcf(c_9557,plain,
! [X0: $i,X1: $i,X2: $i] : ld(X0,ld(X1,mult(X2,X1))) = mult(ld(mult(X1,X0),X2),X1),
inference(superposition,[status(thm)],[c_301,c_50]) ).
tcf(c_11778,plain,
! [X0: $i] : mult(ld(X0,iPr_def_10),mult(sK0,X0)) = ld(X0,mult(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_142,c_552]) ).
tcf(c_11782,plain,
! [X0: $i] : mult(ld(X0,iPr_def_10),mult(sK1,X0)) = ld(X0,mult(sK1,X0)),
inference(superposition,[status(thm)],[c_145,c_552]) ).
tcf(c_13510,plain,
! [X0: $i] : mult(ld(ld(sK1,X0),iPr_def_10),X0) = ld(ld(sK1,X0),X0),
inference(superposition,[status(thm)],[c_49,c_11782]) ).
tcf(c_13515,plain,
mult(ld(mult(iPr_def_10,iPr_def_10),iPr_def_10),sK1) = ld(mult(iPr_def_10,iPr_def_10),sK1),
inference(superposition,[status(thm)],[c_4069,c_11782]) ).
tcf(c_13993,plain,
! [X0: $i] : rd(ld(ld(sK1,X0),X0),X0) = ld(ld(sK1,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_13510,c_52]) ).
tcf(c_14167,plain,
rd(ld(mult(iPr_def_10,iPr_def_10),sK1),sK1) = ld(mult(iPr_def_10,iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_13515,c_52]) ).
tcf(c_15613,plain,
! [X0: $i] : mult(mult(X0,iPr_def_10),rd(sK0,X0)) = rd(mult(X0,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_142,c_1538]) ).
tcf(c_22081,plain,
! [X0: $i,X1: $i] : mult(ld(mult(X0,X1),X0),X0) = ld(X1,X0),
inference(superposition,[status(thm)],[c_50,c_9557]) ).
tcf(c_22633,plain,
! [X0: $i,X1: $i] : ld(ld(X0,X1),X0) = mult(ld(X1,X0),X0),
inference(superposition,[status(thm)],[c_49,c_22081]) ).
tcf(c_22697,plain,
ld(mult(iPr_def_10,iPr_def_10),sK1) = mult(ld(sK1,sK1),sK1),
inference(superposition,[status(thm)],[c_4069,c_22081]) ).
tcf(c_22701,plain,
mult(ld(ld(sK1,iPr_def_10),ld(sK1,iPr_def_10)),ld(sK1,iPr_def_10)) = ld(iPr_def_10,ld(sK1,iPr_def_10)),
inference(superposition,[status(thm)],[c_4310,c_22081]) ).
tcf(c_22729,plain,
! [X0: $i,X1: $i] : ld(mult(X0,X1),X0) = rd(ld(X1,X0),X0),
inference(superposition,[status(thm)],[c_22081,c_52]) ).
tcf(c_22794,plain,
ld(mult(iPr_def_10,iPr_def_10),sK1) = mult(mult(iPr_def_10,iPr_def_10),sK1),
inference(light_normalisation,[status(thm)],[c_22697,c_4077]) ).
tcf(c_22796,plain,
ld(iPr_def_10,ld(sK1,iPr_def_10)) = mult(iPr_def_10,ld(sK1,iPr_def_10)),
inference(light_normalisation,[status(thm)],[c_22701,c_4333]) ).
tcf(c_22806,plain,
rd(ld(mult(iPr_def_10,iPr_def_10),sK1),sK1) = rd(ld(iPr_def_10,iPr_def_10),iPr_def_10),
inference(demodulation,[status(thm)],[c_14167,c_22729]) ).
tcf(c_23486,plain,
! [X0: $i,X1: $i] : rd(X0,mult(ld(X1,X0),X0)) = ld(X0,X1),
inference(superposition,[status(thm)],[c_22633,c_148]) ).
tcf(c_23493,plain,
rd(mult(ld(sK1,sK1),sK1),sK1) = ld(ld(sK1,sK1),iPr_def_10),
inference(superposition,[status(thm)],[c_22633,c_13993]) ).
tcf(c_23494,plain,
rd(mult(mult(iPr_def_10,iPr_def_10),sK1),sK1) = ld(mult(iPr_def_10,iPr_def_10),iPr_def_10),
inference(light_normalisation,[status(thm)],[c_23493,c_4077]) ).
tcf(c_23762,plain,
rd(ld(mult(iPr_def_10,iPr_def_10),sK1),sK1) = ld(sK1,sK1),
inference(superposition,[status(thm)],[c_4069,c_22729]) ).
tcf(c_23790,plain,
! [X0: $i,X1: $i] : rd(X0,rd(ld(X1,X0),X0)) = mult(X0,X1),
inference(superposition,[status(thm)],[c_22729,c_148]) ).
tcf(c_23797,plain,
ld(mult(iPr_def_10,iPr_def_10),iPr_def_10) = mult(iPr_def_10,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_23762,c_4077,c_22794,c_22806,c_23494]) ).
tcf(c_24271,plain,
rd(ld(iPr_def_10,iPr_def_10),iPr_def_10) = mult(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_23797,c_22729]) ).
tcf(c_24274,plain,
mult(mult(iPr_def_10,iPr_def_10),iPr_def_10) = ld(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_24271,c_51]) ).
tcf(c_24332,plain,
mult(ld(iPr_def_10,iPr_def_10),mult(iPr_def_10,iPr_def_10)) = ld(iPr_def_10,ld(iPr_def_10,iPr_def_10)),
inference(superposition,[status(thm)],[c_24274,c_552]) ).
tcf(c_24453,plain,
mult(iPr_def_10,mult(iPr_def_10,ld(sK1,iPr_def_10))) = ld(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_22796,c_49]) ).
tcf(c_24455,plain,
rd(ld(sK1,iPr_def_10),mult(iPr_def_10,ld(sK1,iPr_def_10))) = iPr_def_10,
inference(superposition,[status(thm)],[c_22796,c_148]) ).
tcf(c_24479,plain,
rd(iPr_def_10,ld(ld(sK1,iPr_def_10),iPr_def_10)) = ld(iPr_def_10,ld(sK1,iPr_def_10)),
inference(superposition,[status(thm)],[c_13510,c_23486]) ).
tcf(c_24483,plain,
! [X0: $i,X1: $i] : ld(X0,rd(X0,X1)) = rd(X0,mult(X1,X0)),
inference(superposition,[status(thm)],[c_146,c_23486]) ).
tcf(c_24530,plain,
rd(ld(sK1,iPr_def_10),mult(mult(iPr_def_10,ld(sK1,iPr_def_10)),ld(sK1,iPr_def_10))) = ld(ld(sK1,iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_22796,c_23486]) ).
tcf(c_24574,plain,
rd(iPr_def_10,ld(ld(sK1,iPr_def_10),iPr_def_10)) = mult(iPr_def_10,ld(sK1,iPr_def_10)),
inference(light_normalisation,[status(thm)],[c_24479,c_22796]) ).
tcf(c_24961,plain,
rd(iPr_def_10,mult(iPr_def_10,iPr_def_10)) = mult(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_24271,c_23790]) ).
tcf(c_25312,plain,
mult(mult(iPr_def_10,iPr_def_10),mult(iPr_def_10,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_24961,c_51]) ).
tcf(c_25345,plain,
mult(mult(mult(iPr_def_10,iPr_def_10),iPr_def_10),rd(iPr_def_10,mult(iPr_def_10,iPr_def_10))) = rd(iPr_def_10,mult(iPr_def_10,iPr_def_10)),
inference(superposition,[status(thm)],[c_25312,c_1538]) ).
tcf(c_25363,plain,
ld(iPr_def_10,ld(iPr_def_10,iPr_def_10)) = mult(iPr_def_10,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_25345,c_24274,c_24332,c_24961]) ).
tcf(c_25602,plain,
mult(mult(iPr_def_10,iPr_def_10),rd(ld(sK1,iPr_def_10),iPr_def_10)) = rd(ld(sK1,iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_24453,c_1538]) ).
tcf(c_25616,plain,
mult(mult(iPr_def_10,iPr_def_10),ld(sK1,iPr_def_10)) = ld(sK1,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_25602,c_4332]) ).
tcf(c_25965,plain,
mult(iPr_def_10,mult(iPr_def_10,iPr_def_10)) = ld(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_25363,c_49]) ).
tcf(c_26429,plain,
! [X0: $i,X1: $i] : mult(X0,rd(X0,mult(X1,X0))) = rd(X0,X1),
inference(superposition,[status(thm)],[c_24483,c_49]) ).
tcf(c_26432,plain,
! [X0: $i,X1: $i] : rd(rd(X0,X1),rd(X0,mult(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_24483,c_148]) ).
tcf(c_26868,plain,
mult(iPr_def_10,mult(iPr_def_10,iPr_def_10)) = rd(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_24961,c_26429]) ).
tcf(c_27054,plain,
ld(iPr_def_10,iPr_def_10) = rd(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_25965,c_26868]) ).
tcf(c_27067,plain,
ld(iPr_def_10,mult(iPr_def_11,iPr_def_10)) = mult(rd(iPr_def_10,iPr_def_10),iPr_def_12),
inference(demodulation,[status(thm)],[c_2342,c_27054]) ).
tcf(c_30105,plain,
rd(ld(sK1,iPr_def_10),ld(sK1,iPr_def_10)) = mult(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_25616,c_52]) ).
tcf(c_30722,plain,
rd(iPr_def_10,rd(ld(sK1,iPr_def_10),mult(mult(iPr_def_10,ld(sK1,iPr_def_10)),ld(sK1,iPr_def_10)))) = ld(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_24455,c_26432]) ).
tcf(c_30884,plain,
mult(iPr_def_10,ld(sK1,iPr_def_10)) = ld(sK1,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_30722,c_24530,c_24574]) ).
tcf(c_30934,plain,
rd(ld(sK1,iPr_def_10),ld(sK1,iPr_def_10)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_24455,c_30884]) ).
tcf(c_30937,plain,
mult(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_30105,c_30934]) ).
tcf(c_30950,plain,
rd(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_24961,c_30937]) ).
tcf(c_30990,plain,
ld(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_27054,c_30950]) ).
tcf(c_34181,plain,
! [X0: $i] : mult(mult(iPr_def_10,rd(X0,iPr_def_10)),iPr_def_10) = rd(mult(iPr_def_10,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_30937,c_1524]) ).
tcf(c_34193,plain,
mult(iPr_def_10,rd(sK0,iPr_def_10)) = rd(mult(iPr_def_10,iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_30937,c_15613]) ).
tcf(c_34910,plain,
mult(mult(iPr_def_10,sK0),iPr_def_10) = mult(iPr_def_10,mult(iPr_def_10,iPr_def_12)),
inference(superposition,[status(thm)],[c_30990,c_538]) ).
tcf(c_34912,plain,
ld(iPr_def_10,mult(iPr_def_11,iPr_def_10)) = mult(iPr_def_10,mult(sK0,iPr_def_10)),
inference(superposition,[status(thm)],[c_30990,c_11778]) ).
tcf(c_34914,plain,
ld(iPr_def_10,mult(iPr_def_11,iPr_def_10)) = mult(iPr_def_10,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_34912,c_143,c_27067]) ).
tcf(c_34916,plain,
mult(iPr_def_10,mult(iPr_def_10,iPr_def_12)) = mult(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_34910,c_142]) ).
tcf(c_46985,plain,
mult(mult(iPr_def_10,rd(sK0,iPr_def_10)),iPr_def_10) = mult(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_34193,c_51]) ).
tcf(c_48841,plain,
mult(iPr_def_10,iPr_def_11) = rd(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_46985,c_142,c_34181]) ).
tcf(c_48848,plain,
ld(mult(iPr_def_10,iPr_def_11),iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_48841,c_146]) ).
tcf(c_48849,plain,
mult(mult(iPr_def_10,iPr_def_11),iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_48841,c_51]) ).
tcf(c_48959,plain,
ld(iPr_def_10,mult(iPr_def_11,iPr_def_10)) = mult(iPr_def_11,mult(iPr_def_10,iPr_def_10)),
inference(superposition,[status(thm)],[c_48848,c_301]) ).
tcf(c_48960,plain,
mult(iPr_def_10,iPr_def_12) = mult(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_48959,c_30937,c_34914]) ).
tcf(c_48967,plain,
mult(iPr_def_10,mult(iPr_def_10,iPr_def_12)) = mult(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_34916,c_48960]) ).
tcf(c_49002,plain,
mult(ld(iPr_def_10,iPr_def_10),mult(iPr_def_11,iPr_def_10)) = ld(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_48849,c_552]) ).
tcf(c_49029,plain,
mult(iPr_def_10,iPr_def_12) = sK0,
inference(light_normalisation,[status(thm)],[c_49002,c_140,c_30990,c_48960,c_48967]) ).
tcf(c_49077,plain,
rd(sK0,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_49029,c_52]) ).
tcf(c_49101,plain,
ld(mult(mult(iPr_def_10,iPr_def_10),sK0),mult(iPr_def_10,sK0)) = iPr_def_10,
inference(superposition,[status(thm)],[c_49029,c_1988]) ).
tcf(c_49105,plain,
ld(iPr_def_11,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_49101,c_142,c_30937]) ).
tcf(c_49181,plain,
mult(mult(iPr_def_10,iPr_def_10),sK0) = rd(mult(iPr_def_10,sK0),iPr_def_10),
inference(superposition,[status(thm)],[c_49077,c_4691]) ).
tcf(c_49182,plain,
mult(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_49181,c_142,c_30937,c_48841]) ).
tcf(c_49184,plain,
mult(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_48849,c_49182]) ).
tcf(c_49235,plain,
ld(iPr_def_10,iPr_def_11) = mult(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_49105,c_22633]) ).
tcf(c_49247,plain,
sK0 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_49235,c_140,c_49182]) ).
tcf(c_49382,plain,
mult(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_83,c_49247]) ).
tcf(c_49384,plain,
( ( iPr_def_11 != iPr_def_12 )
| ( iPr_def_11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_84,c_49247]) ).
tcf(c_49385,plain,
iPr_def_11 != iPr_def_12,
inference(equality_resolution_simp,[status(thm)],[c_49384]) ).
tcf(c_49386,plain,
iPr_def_11 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_49382,c_49184]) ).
tcf(c_49387,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_49385,c_49386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 15:32:57 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 17.44/5.29 % SZS status Started for theBenchmark.p
% 17.44/5.29 % SZS status Theorem for theBenchmark.p
% 17.44/5.29
% 17.44/5.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.44/5.29
% 17.44/5.29 % ------ iProver source info
% 17.44/5.29
% 17.44/5.29 % git: date: 2026-07-19 20:42:38 +0200
% 17.44/5.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.44/5.29 % git: non_committed_changes: false
% 17.44/5.29
% 17.44/5.29 % ------ Parsing...
% 17.44/5.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.44/5.29
% 17.44/5.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 17.44/5.29
% 17.44/5.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.44/5.29
% 17.44/5.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 17.44/5.29 % ------ Proving...
% 17.44/5.29 % ------ Problem Properties
% 17.44/5.29
% 17.44/5.29 %
% 17.44/5.29 % clauses 9
% 17.44/5.29 % conjectures 1
% 17.44/5.29 % EPR 1
% 17.44/5.29 % Horn 9
% 17.44/5.29 % unary 8
% 17.44/5.29 % binary 1
% 17.44/5.29 % lits 10
% 17.44/5.29 % lits eq 10
% 17.44/5.29 % fd_pure 0
% 17.44/5.29 % fd_pseudo 0
% 17.44/5.29 % fd_cond 0
% 17.44/5.29 % fd_pseudo_cond 0
% 17.44/5.29 % AC symbols 0
% 17.44/5.29
% 17.44/5.29 % ------ Schedule dynamic 5 is on
% 17.44/5.29
% 17.44/5.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.44/5.29
% 17.44/5.29
% 17.44/5.29 % ------
% 17.44/5.29 % Current options:
% 17.44/5.29 % ------
% 17.44/5.29
% 17.44/5.29
% 17.44/5.29 %
% 17.44/5.29
% 17.44/5.29 % ------ Proving...
% 17.44/5.29 %
% 17.44/5.29
% 17.44/5.29 % SZS status Theorem for theBenchmark.p
% 17.44/5.29
% 17.44/5.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.44/5.29
% 17.44/5.29
%------------------------------------------------------------------------------