%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP682+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 01:35:11 PM UTC 2026
% Result : Theorem 10.60s 2.20s
% Output : CNFRefutation 10.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of formulae : 126 ( 118 unt; 0 def)
% Number of atoms : 134 ( 133 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 6 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 281 ( 0 sgn 278 !; 3 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X0,X1,X2,X3] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(ld(X3,mult(X3,X1)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,axiom,
! [X0,X1,X2,X3] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,rd(mult(X2,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f7,axiom,
! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = rd(mult(rd(X1,X1),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f8,conjecture,
! [X0,X1,X2] :
( ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2))
& ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2))
& ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ld(X0,mult(X0,X2)) != ld(rd(X0,X1),mult(rd(X0,X1),X2))
| ld(ld(X0,X1),mult(ld(X0,X1),X2)) != ld(X0,mult(X0,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
( ld(sK0,mult(sK0,sK2)) != ld(rd(sK0,sK1),mult(rd(sK0,sK1),sK2))
| ld(ld(sK0,sK1),mult(ld(sK0,sK1),sK2)) != ld(sK0,mult(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
fof(f12,plain,
( ld(sK0,mult(sK0,sK2)) != ld(rd(sK0,sK1),mult(rd(sK0,sK1),sK2))
| ld(ld(sK0,sK1),mult(ld(sK0,sK1),sK2)) != ld(sK0,mult(sK0,sK2)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f13,plain,
! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = rd(mult(rd(X1,X1),X0),X0),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X2,X3,X0,X1] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(ld(X3,mult(X3,X1)),X0),
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
! [X2,X3,X0,X1] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,rd(mult(X2,X0),X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f18,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0),
inference(cnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_49,negated_conjecture,
( ( ld(rd(sK0,sK1),mult(rd(sK0,sK1),sK2)) != ld(sK0,mult(sK0,sK2)) )
| ( ld(ld(sK0,sK1),mult(ld(sK0,sK1),sK2)) != ld(sK0,mult(sK0,sK2)) ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(cnf_transformation,[],[f13]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(cnf_transformation,[],[f14]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,X1)) = mult(X0,ld(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_53,plain,
! [X0: $i] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[],[f18]) ).
tcf(c_56,plain,
! [X0: $i] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_82,plain,
! [X0: $i] : mult(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_56,c_55]) ).
tcf(c_83,plain,
! [X0: $i] : mult(X0,ld(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_53,c_52]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : mult(rd(rd(X0,X0),X1),X1) = mult(X0,ld(X0,ld(X1,X1))),
inference(demodulation,[status(thm)],[c_50,c_52,c_55]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(demodulation,[status(thm)],[c_54,c_55]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(demodulation,[status(thm)],[c_51,c_52]) ).
tcf(c_87,plain,
( ( mult(rd(sK0,sK1),ld(rd(sK0,sK1),sK2)) != mult(sK0,ld(sK0,sK2)) )
| ( mult(ld(sK0,sK1),ld(ld(sK0,sK1),sK2)) != mult(sK0,ld(sK0,sK2)) ) ),
inference(demodulation,[status(thm)],[c_49,c_52]) ).
tcf(c_156,plain,
! [X0: $i] : mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[c_83,c_52]) ).
tcf(c_159,plain,
! [X0: $i] : mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(superposition,[status(thm)],[c_82,c_55]) ).
tcf(c_160,plain,
! [X0: $i] : mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[c_83,c_55]) ).
tcf(c_167,plain,
! [X0: $i] : ld(X0,X0) = rd(X0,X0),
inference(demodulation,[status(thm)],[c_159,c_84,c_156]) ).
tcf(c_168,plain,
! [X0: $i] : mult(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_82,c_167]) ).
tcf(c_171,plain,
! [X0: $i] : mult(ld(X0,X0),ld(ld(X0,X0),X0)) = ld(ld(X0,X0),X0),
inference(superposition,[status(thm)],[c_168,c_52]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] : mult(rd(ld(X0,X0),X1),X1) = mult(X0,ld(X0,ld(X1,X1))),
inference(light_normalisation,[status(thm)],[c_84,c_167]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
inference(superposition,[status(thm)],[c_83,c_85]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(ld(X0,X0),mult(rd(X0,X2),X2)),
inference(superposition,[status(thm)],[c_168,c_85]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),ld(X2,X2)),ld(X2,X2)) = mult(X0,mult(rd(X1,X2),X2)),
inference(superposition,[status(thm)],[c_167,c_85]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),ld(X1,X1)) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_83,c_86]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_168,c_86]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(X0,ld(X0,ld(X2,X2)))),
inference(demodulation,[status(thm)],[c_183,c_175]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i] : mult(rd(X0,ld(X1,X1)),ld(X1,X1)) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(superposition,[status(thm)],[c_167,c_345]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i] : mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = mult(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[c_156,c_345]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] : mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_356,c_83]) ).
tcf(c_370,plain,
! [X0: $i] : mult(X0,mult(X0,ld(X0,ld(X0,X0)))) = rd(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[c_160,c_351]) ).
tcf(c_371,plain,
! [X0: $i] : rd(X0,ld(X0,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_370,c_83,c_156]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))) = mult(rd(mult(X0,X1),X2),X2),
inference(superposition,[status(thm)],[c_371,c_85]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,rd(X2,X0))),rd(X1,rd(X2,X0))) = mult(ld(X0,X0),X0),
inference(superposition,[status(thm)],[c_369,c_186]) ).
tcf(c_647,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,rd(X2,X0))),rd(X1,rd(X2,X0))) = X0,
inference(light_normalisation,[status(thm)],[c_624,c_168]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(superposition,[status(thm)],[c_83,c_218]) ).
tcf(c_863,plain,
! [X0: $i] : ld(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_171,c_836]) ).
tcf(c_915,plain,
! [X0: $i,X1: $i] : mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),ld(X1,X1)) = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[c_863,c_218]) ).
tcf(c_951,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(ld(X0,X1),X2),ld(ld(ld(X0,X1),X2),X0)) = mult(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[c_836,c_218]) ).
tcf(c_957,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(ld(X0,X1),X2),ld(ld(ld(X0,X1),X2),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_951,c_83]) ).
tcf(c_998,plain,
! [X0: $i,X1: $i] : mult(rd(ld(X0,X0),rd(X1,X0)),rd(X1,X0)) = ld(X0,X0),
inference(superposition,[status(thm)],[c_371,c_647]) ).
tcf(c_1279,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(mult(X0,ld(X0,X1)),X2),ld(ld(mult(X0,ld(X0,X1)),X2),X0)) = X0,
inference(superposition,[status(thm)],[c_52,c_957]) ).
tcf(c_1280,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[c_863,c_957]) ).
tcf(c_1317,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(rd(X1,X0),rd(X1,X0)))) = ld(X0,X0),
inference(demodulation,[status(thm)],[c_998,c_175]) ).
tcf(c_1324,plain,
! [X0: $i] : mult(ld(X0,X0),ld(ld(X0,X0),ld(X0,X0))) = ld(ld(X0,X0),ld(X0,X0)),
inference(superposition,[status(thm)],[c_371,c_1317]) ).
tcf(c_1741,plain,
! [X0: $i] : mult(mult(X0,ld(X0,ld(X0,X0))),ld(ld(X0,X0),ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[c_1280,c_218]) ).
tcf(c_1743,plain,
! [X0: $i] : ld(ld(X0,X0),ld(X0,X0)) = ld(X0,X0),
inference(light_normalisation,[status(thm)],[c_1741,c_156,c_1324]) ).
tcf(c_1840,plain,
! [X0: $i,X1: $i] : mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),ld(X1,X1)) = mult(ld(X0,X0),ld(ld(X0,X0),X1)),
inference(superposition,[status(thm)],[c_1743,c_218]) ).
tcf(c_1841,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),ld(X2,X2)),ld(X2,X2)) = mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))),
inference(superposition,[status(thm)],[c_1743,c_190]) ).
tcf(c_1850,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),X2),X2) = mult(X0,mult(rd(X1,X2),X2)),
inference(light_normalisation,[status(thm)],[c_1841,c_190,c_421]) ).
tcf(c_1851,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X0),ld(ld(X0,X0),X1)) = mult(X0,ld(X0,X1)),
inference(light_normalisation,[status(thm)],[c_1840,c_915]) ).
tcf(c_1899,plain,
! [X0: $i,X1: $i] : mult(mult(rd(X0,X1),X1),X1) = mult(X0,mult(rd(X1,X1),X1)),
inference(superposition,[status(thm)],[c_55,c_1850]) ).
tcf(c_1902,plain,
! [X0: $i,X1: $i] : mult(X0,mult(rd(ld(X0,X0),X1),X1)) = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[c_83,c_1850]) ).
tcf(c_1907,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X0),mult(rd(X0,X1),X1)) = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[c_168,c_1850]) ).
tcf(c_1945,plain,
! [X0: $i,X1: $i] : mult(X0,mult(X0,ld(X0,ld(X1,X1)))) = mult(rd(X0,X1),X1),
inference(light_normalisation,[status(thm)],[c_1902,c_175]) ).
tcf(c_1956,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,X2),X2),
inference(demodulation,[status(thm)],[c_186,c_1907]) ).
tcf(c_2106,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
inference(superposition,[status(thm)],[c_1851,c_86]) ).
tcf(c_2110,plain,
! [X0: $i,X1: $i] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[c_1851,c_222]) ).
tcf(c_2126,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(X2,ld(X2,X2)))),
inference(demodulation,[status(thm)],[c_218,c_2106]) ).
tcf(c_2127,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(ld(X2,X2),X2))),
inference(demodulation,[status(thm)],[c_222,c_2106]) ).
tcf(c_2133,plain,
( ( mult(sK0,ld(sK0,mult(ld(sK2,sK2),sK2))) != mult(sK0,ld(sK0,sK2)) )
| ( mult(rd(sK0,sK1),ld(rd(sK0,sK1),sK2)) != mult(sK0,ld(sK0,sK2)) ) ),
inference(demodulation,[status(thm)],[c_87,c_2127]) ).
tcf(c_2134,plain,
mult(rd(sK0,sK1),ld(rd(sK0,sK1),sK2)) != mult(sK0,ld(sK0,sK2)),
inference(ground_joinability,[status(thm)],[c_2133,c_168]) ).
tcf(c_2171,plain,
! [X0: $i,X1: $i] : mult(mult(rd(X0,X1),X1),X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[c_1899,c_167,c_168]) ).
tcf(c_2173,plain,
! [X0: $i,X1: $i] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(ld(X0,X0),X1),
inference(superposition,[status(thm)],[c_175,c_2171]) ).
tcf(c_2187,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X0),X1) = mult(X0,ld(X0,X1)),
inference(light_normalisation,[status(thm)],[c_2173,c_2110]) ).
tcf(c_2193,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(ld(X0,X0),X1))) = mult(X0,ld(X0,X1)),
inference(demodulation,[status(thm)],[c_1851,c_2187]) ).
tcf(c_2227,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,ld(X0,X1)),X2),X2) = mult(ld(X0,X0),mult(rd(X1,X2),X2)),
inference(superposition,[status(thm)],[c_2187,c_1850]) ).
tcf(c_2616,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,mult(X0,X1))) = mult(X0,X1),
inference(superposition,[status(thm)],[c_83,c_2106]) ).
tcf(c_2633,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,ld(X0,X1)),X2),X2) = rd(mult(X0,ld(X0,mult(X1,X2))),X2),
inference(superposition,[status(thm)],[c_2106,c_55]) ).
tcf(c_2647,plain,
! [X0: $i,X1: $i] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,X1),
inference(light_normalisation,[status(thm)],[c_2616,c_52]) ).
tcf(c_2649,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X0),mult(rd(X1,X2),X2)) = rd(mult(X0,ld(X0,mult(X1,X2))),X2),
inference(light_normalisation,[status(thm)],[c_2633,c_2227]) ).
tcf(c_2657,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(demodulation,[status(thm)],[c_1945,c_2647]) ).
tcf(c_2658,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),X2),X2) = mult(X0,mult(X1,ld(X2,X2))),
inference(demodulation,[status(thm)],[c_1850,c_2657]) ).
tcf(c_2662,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X1,X1)) = rd(mult(X0,X1),X1),
inference(demodulation,[status(thm)],[c_55,c_2657]) ).
tcf(c_2830,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),ld(X1,X1)) = rd(mult(X0,ld(X1,X1)),X1),
inference(superposition,[status(thm)],[c_2657,c_2662]) ).
tcf(c_3046,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(rd(X1,X2),rd(X1,X2))) = mult(X0,ld(X2,X2)),
inference(demodulation,[status(thm)],[c_1956,c_2657]) ).
tcf(c_3067,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),ld(X1,X1)) = rd(X0,X1),
inference(superposition,[status(thm)],[c_3046,c_83]) ).
tcf(c_3577,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(X1,ld(X2,X2))),
inference(demodulation,[status(thm)],[c_2658,c_2657]) ).
tcf(c_3614,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X0,mult(X1,ld(X2,X2)))) = mult(X0,mult(ld(X0,X1),ld(X2,X2))),
inference(superposition,[status(thm)],[c_3577,c_2106]) ).
tcf(c_3719,plain,
! [X0: $i,X1: $i] : rd(mult(X0,ld(X1,X1)),X1) = rd(X0,X1),
inference(light_normalisation,[status(thm)],[c_2830,c_3067]) ).
tcf(c_3722,plain,
! [X0: $i,X1: $i,X2: $i] : rd(mult(X0,ld(X0,mult(X1,ld(X2,X2)))),X2) = rd(mult(X0,ld(X0,X1)),X2),
inference(superposition,[status(thm)],[c_2106,c_3719]) ).
tcf(c_3736,plain,
! [X0: $i,X1: $i,X2: $i] : rd(mult(X0,mult(ld(X0,X1),ld(X2,X2))),X2) = rd(mult(X0,ld(X0,X1)),X2),
inference(light_normalisation,[status(thm)],[c_3722,c_3614]) ).
tcf(c_4657,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(mult(X0,mult(X0,ld(X0,X1))),X2),ld(ld(mult(X0,mult(X0,ld(X0,X1))),X2),X0)) = X0,
inference(superposition,[status(thm)],[c_52,c_1279]) ).
tcf(c_4673,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(mult(X0,X1),X2),ld(ld(mult(X0,X1),X2),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4657,c_2647]) ).
tcf(c_4710,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),ld(X0,X2))) = ld(X0,X2),
inference(superposition,[status(thm)],[c_836,c_4673]) ).
tcf(c_5087,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(ld(X0,X0),X1))) = ld(ld(X0,X0),X1),
inference(superposition,[status(thm)],[c_863,c_4710]) ).
tcf(c_5105,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X1)))) = ld(X0,X1),
inference(superposition,[status(thm)],[c_4710,c_2187]) ).
tcf(c_5106,plain,
! [X0: $i,X1: $i] : ld(ld(X0,X0),X1) = mult(X0,ld(X0,X1)),
inference(light_normalisation,[status(thm)],[c_5087,c_2193]) ).
tcf(c_5631,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(X0,X1))) = ld(X0,X1),
inference(demodulation,[status(thm)],[c_5105,c_52,c_2647,c_5106]) ).
tcf(c_5652,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X0,mult(ld(X0,X1),X2))) = mult(ld(X0,X1),X2),
inference(superposition,[status(thm)],[c_5631,c_2106]) ).
tcf(c_6114,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),ld(mult(X0,X1),X0)) = X0,
inference(superposition,[status(thm)],[c_4673,c_5652]) ).
tcf(c_6261,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),ld(mult(X0,X1),mult(X0,X2))) = mult(X0,X2),
inference(superposition,[status(thm)],[c_6114,c_2106]) ).
tcf(c_6791,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X0,mult(mult(X0,X1),X2))) = mult(mult(X0,X1),X2),
inference(superposition,[status(thm)],[c_6114,c_6261]) ).
tcf(c_7645,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,mult(ld(X0,X2),ld(X2,X2))),
inference(demodulation,[status(thm)],[c_2126,c_3614]) ).
tcf(c_7972,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(demodulation,[status(thm)],[c_2127,c_83,c_2187]) ).
tcf(c_7974,plain,
! [X0: $i,X1: $i] : mult(X0,mult(ld(X0,X1),ld(X1,X1))) = mult(X0,ld(X0,X1)),
inference(demodulation,[status(thm)],[c_7645,c_7972]) ).
tcf(c_7993,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = mult(X0,ld(X0,X2)),
inference(superposition,[status(thm)],[c_52,c_7972]) ).
tcf(c_9465,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(X0,rd(X1,X2)),ld(X2,X2))) = mult(X0,ld(X0,rd(X1,X2))),
inference(superposition,[status(thm)],[c_3046,c_7974]) ).
tcf(c_11828,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(X0,ld(X0,X2)),
inference(demodulation,[status(thm)],[c_7993,c_2106]) ).
tcf(c_11904,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),ld(mult(X0,ld(X0,mult(X0,X1))),X2)) = mult(X0,ld(X0,X2)),
inference(superposition,[status(thm)],[c_11828,c_6791]) ).
tcf(c_11910,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),ld(mult(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(light_normalisation,[status(thm)],[c_11904,c_52,c_2647]) ).
tcf(c_15439,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(X0,X1),ld(X2,X2))) = rd(mult(X0,ld(X0,mult(X1,X2))),X2),
inference(demodulation,[status(thm)],[c_2649,c_2187,c_2657,c_3614]) ).
tcf(c_15459,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(X0,rd(X1,X2)),ld(X2,X2))) = rd(mult(X0,ld(X0,mult(X1,ld(X2,X2)))),X2),
inference(superposition,[status(thm)],[c_2657,c_15439]) ).
tcf(c_15509,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X0,rd(X1,X2))) = rd(mult(X0,ld(X0,X1)),X2),
inference(light_normalisation,[status(thm)],[c_15459,c_3614,c_3736,c_9465]) ).
tcf(c_15811,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,rd(X0,X1))) = rd(X0,X1),
inference(superposition,[status(thm)],[c_83,c_15509]) ).
tcf(c_16290,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(superposition,[status(thm)],[c_15811,c_11910]) ).
tcf(c_16311,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2134,c_16290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP682+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 15:41:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/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
% 0.14/0.43 % Proving...
% 10.60/2.20 % SZS status Started for theBenchmark.p
% 10.60/2.20 % SZS status Theorem for theBenchmark.p
% 10.60/2.20
% 10.60/2.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.60/2.20
% 10.60/2.20 % ------ iProver source info
% 10.60/2.20
% 10.60/2.20 % git: date: 2026-07-19 20:42:38 +0200
% 10.60/2.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.60/2.20 % git: non_committed_changes: false
% 10.60/2.20
% 10.60/2.20 % ------ Parsing...
% 10.60/2.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.60/2.20
% 10.60/2.20 % ------ Preprocessing... sup_sim: 6 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.60/2.20
% 10.60/2.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.60/2.20
% 10.60/2.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.60/2.20 % ------ Proving...
% 10.60/2.20 % ------ Problem Properties
% 10.60/2.20
% 10.60/2.20 %
% 10.60/2.20 % clauses 8
% 10.60/2.20 % conjectures 0
% 10.60/2.20 % EPR 0
% 10.60/2.20 % Horn 8
% 10.60/2.20 % unary 7
% 10.60/2.20 % binary 1
% 10.60/2.20 % lits 9
% 10.60/2.20 % lits eq 9
% 10.60/2.20 % fd_pure 0
% 10.60/2.20 % fd_pseudo 0
% 10.60/2.20 % fd_cond 0
% 10.60/2.20 % fd_pseudo_cond 0
% 10.60/2.20 % AC symbols 0
% 10.60/2.20
% 10.60/2.20 % ------ Schedule dynamic 5 is on
% 10.60/2.20
% 10.60/2.20 % ------ no conjectures: strip conj schedule
% 10.60/2.20
% 10.60/2.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 10.60/2.20
% 10.60/2.20
% 10.60/2.20 % ------
% 10.60/2.20 % Current options:
% 10.60/2.20 % ------
% 10.60/2.20
% 10.60/2.20
% 10.60/2.20 %
% 10.60/2.20
% 10.60/2.20 % ------ Proving...
% 10.60/2.20 %
% 10.60/2.20
% 10.60/2.20 % SZS status Theorem for theBenchmark.p
% 10.60/2.20
% 10.60/2.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.60/2.20
% 10.60/2.20
%------------------------------------------------------------------------------