%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP683+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 01:35:12 PM UTC 2026
% Result : Theorem 10.78s 2.72s
% Output : CNFRefutation 10.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 8
% Syntax : Number of formulae : 118 ( 110 unt; 0 def)
% Number of atoms : 126 ( 125 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 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 : 255 ( 0 sgn 252 !; 3 ?; 214 :)
% 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] :
( mult(rd(mult(X0,X1),X1),X2) = mult(X0,X2)
& mult(X0,ld(X1,mult(X1,X2))) = mult(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( mult(rd(mult(X0,X1),X1),X2) = mult(X0,X2)
& mult(X0,ld(X1,mult(X1,X2))) = mult(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0,X1,X2] :
( mult(X0,X2) != mult(rd(mult(X0,X1),X1),X2)
| mult(X0,ld(X1,mult(X1,X2))) != mult(X0,X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
( mult(sK0,sK2) != mult(rd(mult(sK0,sK1),sK1),sK2)
| mult(sK0,ld(sK1,mult(sK1,sK2))) != 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,
( mult(sK0,sK2) != mult(rd(mult(sK0,sK1),sK1),sK2)
| mult(sK0,ld(sK1,mult(sK1,sK2))) != 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,
( ( mult(sK0,ld(sK1,mult(sK1,sK2))) != mult(sK0,sK2) )
| ( mult(rd(mult(sK0,sK1),sK1),sK2) != 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] : mult(X0,ld(X0,X1)) = ld(X0,mult(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(sK0,mult(sK1,ld(sK1,sK2))) != mult(sK0,sK2) )
| ( mult(mult(rd(sK0,sK1),sK1),sK2) != mult(sK0,sK2) ) ),
inference(demodulation,[status(thm)],[c_49,c_52,c_55]) ).
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_219,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_223,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_340,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_346,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_340]) ).
tcf(c_351,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_340]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] : mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_351,c_83]) ).
tcf(c_365,plain,
! [X0: $i] : mult(X0,mult(X0,ld(X0,ld(X0,X0)))) = rd(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[c_160,c_346]) ).
tcf(c_366,plain,
! [X0: $i] : rd(X0,ld(X0,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_365,c_83,c_156]) ).
tcf(c_426,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_366,c_85]) ).
tcf(c_635,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_364,c_186]) ).
tcf(c_658,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_635,c_168]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(superposition,[status(thm)],[c_83,c_219]) ).
tcf(c_866,plain,
! [X0: $i] : ld(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_171,c_839]) ).
tcf(c_922,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_866,c_219]) ).
tcf(c_966,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_839,c_219]) ).
tcf(c_972,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_966,c_83]) ).
tcf(c_1016,plain,
! [X0: $i,X1: $i] : mult(rd(ld(X0,X0),rd(X1,X0)),rd(X1,X0)) = ld(X0,X0),
inference(superposition,[status(thm)],[c_366,c_658]) ).
tcf(c_1335,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_972]) ).
tcf(c_1336,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[c_866,c_972]) ).
tcf(c_1381,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(rd(X1,X0),rd(X1,X0)))) = ld(X0,X0),
inference(demodulation,[status(thm)],[c_1016,c_175]) ).
tcf(c_1388,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_366,c_1381]) ).
tcf(c_1799,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_1336,c_219]) ).
tcf(c_1801,plain,
! [X0: $i] : ld(ld(X0,X0),ld(X0,X0)) = ld(X0,X0),
inference(light_normalisation,[status(thm)],[c_1799,c_156,c_1388]) ).
tcf(c_1908,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_1801,c_219]) ).
tcf(c_1909,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_1801,c_190]) ).
tcf(c_1918,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_1909,c_190,c_426]) ).
tcf(c_1919,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_1908,c_922]) ).
tcf(c_1978,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_1918]) ).
tcf(c_1981,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_1918]) ).
tcf(c_2024,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_1981,c_175]) ).
tcf(c_2213,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_1919,c_86]) ).
tcf(c_2217,plain,
! [X0: $i,X1: $i] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[c_1919,c_223]) ).
tcf(c_2234,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_223,c_2213]) ).
tcf(c_2289,plain,
! [X0: $i,X1: $i] : mult(mult(rd(X0,X1),X1),X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[c_1978,c_167,c_168]) ).
tcf(c_2291,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_2289]) ).
tcf(c_2292,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,mult(rd(X1,X2),X2)),X2) = mult(mult(X0,X1),X2),
inference(superposition,[status(thm)],[c_1918,c_2289]) ).
tcf(c_2305,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X0),X1) = mult(X0,ld(X0,X1)),
inference(light_normalisation,[status(thm)],[c_2291,c_2217]) ).
tcf(c_2311,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(ld(X0,X0),X1))) = mult(X0,ld(X0,X1)),
inference(demodulation,[status(thm)],[c_1919,c_2305]) ).
tcf(c_2770,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,mult(X0,X1))) = mult(X0,X1),
inference(superposition,[status(thm)],[c_83,c_2213]) ).
tcf(c_2801,plain,
! [X0: $i,X1: $i] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,X1),
inference(light_normalisation,[status(thm)],[c_2770,c_52]) ).
tcf(c_2811,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(demodulation,[status(thm)],[c_2024,c_2801]) ).
tcf(c_2812,plain,
( ( mult(sK0,mult(sK1,ld(sK1,sK2))) != mult(sK0,sK2) )
| ( mult(mult(sK0,ld(sK1,sK1)),sK2) != mult(sK0,sK2) ) ),
inference(demodulation,[status(thm)],[c_87,c_2811]) ).
tcf(c_2816,plain,
! [X0: $i,X1: $i] : mult(mult(X0,ld(X1,X1)),X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[c_2289,c_2811]) ).
tcf(c_2817,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X1,X1)) = rd(mult(X0,X1),X1),
inference(demodulation,[status(thm)],[c_55,c_2811]) ).
tcf(c_3045,plain,
! [X0: $i,X1: $i] : mult(mult(X0,ld(X1,X1)),X1) = mult(mult(X0,X1),ld(X1,X1)),
inference(superposition,[status(thm)],[c_2817,c_2811]) ).
tcf(c_3047,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),ld(X1,X1)) = mult(X0,X1),
inference(light_normalisation,[status(thm)],[c_3045,c_2816]) ).
tcf(c_3114,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),ld(mult(X0,X1),ld(X1,X1))) = ld(mult(X0,X1),mult(X0,X1)),
inference(superposition,[status(thm)],[c_3047,c_52]) ).
tcf(c_3345,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,mult(X1,ld(X2,X2))),X2) = mult(mult(X0,X1),X2),
inference(demodulation,[status(thm)],[c_2292,c_2811]) ).
tcf(c_3354,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,mult(X1,ld(X1,ld(X2,X2)))),X2) = mult(mult(X0,ld(X1,X1)),X2),
inference(superposition,[status(thm)],[c_2305,c_3345]) ).
tcf(c_4722,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_1335]) ).
tcf(c_4738,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_4722,c_2801]) ).
tcf(c_4775,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_839,c_4738]) ).
tcf(c_5306,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(ld(X0,X0),X1))) = ld(ld(X0,X0),X1),
inference(superposition,[status(thm)],[c_866,c_4775]) ).
tcf(c_5324,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X1)))) = ld(X0,X1),
inference(superposition,[status(thm)],[c_4775,c_2305]) ).
tcf(c_5325,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = ld(ld(X0,X0),X1),
inference(light_normalisation,[status(thm)],[c_5306,c_2311]) ).
tcf(c_5863,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(X0,X1))) = ld(X0,X1),
inference(demodulation,[status(thm)],[c_5324,c_52,c_2801,c_5325]) ).
tcf(c_5884,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_5863,c_2213]) ).
tcf(c_6353,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),ld(mult(X0,X1),X0)) = X0,
inference(superposition,[status(thm)],[c_4738,c_5884]) ).
tcf(c_6585,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_6353,c_2213]) ).
tcf(c_7154,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_6353,c_6585]) ).
tcf(c_8287,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_2234,c_83,c_2305]) ).
tcf(c_8308,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_8287]) ).
tcf(c_11949,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_8308,c_2213]) ).
tcf(c_12024,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_11949,c_7154]) ).
tcf(c_12029,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_12024,c_52,c_2801]) ).
tcf(c_12050,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,X1),mult(X0,X1)),
inference(demodulation,[status(thm)],[c_3114,c_12029]) ).
tcf(c_12811,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,ld(X1,X1))),X2) = mult(mult(X0,X1),ld(mult(X0,X1),X2)),
inference(superposition,[status(thm)],[c_12050,c_2305]) ).
tcf(c_12822,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,ld(X1,X1))),X2) = mult(X0,ld(X0,X2)),
inference(light_normalisation,[status(thm)],[c_12811,c_12029]) ).
tcf(c_13221,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X0,mult(X1,ld(X1,X2)))) = mult(X0,ld(X0,X2)),
inference(demodulation,[status(thm)],[c_12822,c_2213,c_2305]) ).
tcf(c_13273,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,mult(X2,ld(X2,X1))),
inference(superposition,[status(thm)],[c_13221,c_2801]) ).
tcf(c_13292,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(X1,ld(X1,X2))) = mult(X0,X2),
inference(light_normalisation,[status(thm)],[c_13273,c_2801]) ).
tcf(c_13309,plain,
mult(mult(sK0,ld(sK1,sK1)),sK2) != mult(sK0,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_2812,c_13292]) ).
tcf(c_20264,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X1,X1)),X2) = mult(X0,X2),
inference(demodulation,[status(thm)],[c_3354,c_2816,c_13292]) ).
tcf(c_20265,plain,
mult(sK0,sK2) != mult(sK0,sK2),
inference(demodulation,[status(thm)],[c_13309,c_20264]) ).
tcf(c_20271,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_20265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP683+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 15:41:26 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 10.78/2.72 % SZS status Started for theBenchmark.p
% 10.78/2.72 % SZS status Theorem for theBenchmark.p
% 10.78/2.72
% 10.78/2.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.78/2.72
% 10.78/2.72 % ------ iProver source info
% 10.78/2.72
% 10.78/2.72 % git: date: 2026-07-19 20:42:38 +0200
% 10.78/2.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.78/2.72 % git: non_committed_changes: false
% 10.78/2.72
% 10.78/2.72 % ------ Parsing...
% 10.78/2.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.78/2.72
% 10.78/2.72 % ------ Preprocessing... sup_sim: 6 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.78/2.72
% 10.78/2.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.78/2.72
% 10.78/2.72 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.78/2.72 % ------ Proving...
% 10.78/2.72 % ------ Problem Properties
% 10.78/2.72
% 10.78/2.72 %
% 10.78/2.72 % clauses 8
% 10.78/2.72 % conjectures 0
% 10.78/2.72 % EPR 0
% 10.78/2.72 % Horn 8
% 10.78/2.72 % unary 7
% 10.78/2.72 % binary 1
% 10.78/2.72 % lits 9
% 10.78/2.72 % lits eq 9
% 10.78/2.72 % fd_pure 0
% 10.78/2.73 % fd_pseudo 0
% 10.78/2.73 % fd_cond 0
% 10.78/2.73 % fd_pseudo_cond 0
% 10.78/2.73 % AC symbols 0
% 10.78/2.73
% 10.78/2.73 % ------ Schedule dynamic 5 is on
% 10.78/2.73
% 10.78/2.73 % ------ no conjectures: strip conj schedule
% 10.78/2.73
% 10.78/2.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 10.78/2.73
% 10.78/2.73
% 10.78/2.73 % ------
% 10.78/2.73 % Current options:
% 10.78/2.73 % ------
% 10.78/2.73
% 10.78/2.73
% 10.78/2.73 %
% 10.78/2.73
% 10.78/2.73 % ------ Proving...
% 10.78/2.73 %
% 10.78/2.73
% 10.78/2.73 % SZS status Theorem for theBenchmark.p
% 10.78/2.73
% 10.78/2.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.78/2.73
% 10.78/2.73
%------------------------------------------------------------------------------