%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP685+1 : 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 : n016.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 10.30s 2.75s
% Output : CNFRefutation 10.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 8
% Syntax : Number of formulae : 142 ( 133 unt; 0 def)
% Number of atoms : 151 ( 150 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 19 ~; 7 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 299 ( 0 sgn 296 !; 3 ?; 258 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f8,conjecture,
! [X0,X1,X2] :
( rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(X0,X2),X2)
& rd(mult(X0,ld(X1,X2)),ld(X1,X2)) = rd(mult(X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(X0,X2),X2)
& rd(mult(X0,ld(X1,X2)),ld(X1,X2)) = rd(mult(X0,X2),X2) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0,X1,X2] :
( rd(mult(X0,X2),X2) != rd(mult(X0,rd(X1,X2)),rd(X1,X2))
| rd(mult(X0,ld(X1,X2)),ld(X1,X2)) != rd(mult(X0,X2),X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
( rd(mult(sK0,sK2),sK2) != rd(mult(sK0,rd(sK1,sK2)),rd(sK1,sK2))
| rd(mult(sK0,ld(sK1,sK2)),ld(sK1,sK2)) != rd(mult(sK0,sK2),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
fof(f12,plain,
( rd(mult(sK0,sK2),sK2) != rd(mult(sK0,rd(sK1,sK2)),rd(sK1,sK2))
| rd(mult(sK0,ld(sK1,sK2)),ld(sK1,sK2)) != rd(mult(sK0,sK2),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,
( ( rd(mult(sK0,rd(sK1,sK2)),rd(sK1,sK2)) != rd(mult(sK0,sK2),sK2) )
| ( rd(mult(sK0,ld(sK1,sK2)),ld(sK1,sK2)) != rd(mult(sK0,sK2),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,rd(sK1,sK2)),rd(sK1,sK2)) != mult(rd(sK0,sK2),sK2) )
| ( mult(rd(sK0,ld(sK1,sK2)),ld(sK1,sK2)) != mult(rd(sK0,sK2),sK2) ) ),
inference(demodulation,[status(thm)],[c_49,c_55]) ).
tcf(c_155,plain,
! [X0: $i] : mult(rd(X0,X0),ld(rd(X0,X0),X0)) = ld(rd(X0,X0),X0),
inference(superposition,[status(thm)],[c_82,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_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(X0,ld(X0,rd(X0,X0))) = rd(X0,X0),
inference(demodulation,[status(thm)],[c_156,c_167]) ).
tcf(c_169,plain,
! [X0: $i] : mult(X0,rd(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_83,c_167]) ).
tcf(c_172,plain,
! [X0: $i] : mult(rd(X0,rd(X0,X0)),rd(X0,X0)) = rd(X0,rd(X0,X0)),
inference(superposition,[status(thm)],[c_169,c_55]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] : mult(rd(rd(X0,X0),X1),X1) = mult(X0,ld(X0,rd(X1,X1))),
inference(demodulation,[status(thm)],[c_84,c_167]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,X0),mult(rd(X0,X2),X2)),
inference(superposition,[status(thm)],[c_82,c_85]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(rd(X0,X0),X2),X2)),
inference(superposition,[status(thm)],[c_169,c_85]) ).
tcf(c_194,plain,
( ( mult(rd(sK0,sK0),mult(rd(sK0,sK2),sK2)) != mult(rd(sK0,sK2),sK2) )
| ( mult(rd(sK0,ld(sK1,sK2)),ld(sK1,sK2)) != mult(rd(sK0,sK2),sK2) ) ),
inference(demodulation,[status(thm)],[c_87,c_185]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,rd(X1,X1))),X1) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_82,c_86]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),rd(X1,X1)) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_169,c_86]) ).
tcf(c_286,plain,
! [X0: $i] : rd(X0,rd(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_172,c_82,c_185]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(rd(X1,rd(X2,X2)),rd(X2,X2))) = mult(rd(mult(X0,X1),X2),X2),
inference(superposition,[status(thm)],[c_286,c_85]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i] : mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_82,c_185]) ).
tcf(c_484,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,rd(X2,X0))),rd(X1,rd(X2,X0))) = mult(rd(X0,X0),X0),
inference(superposition,[status(thm)],[c_380,c_185]) ).
tcf(c_486,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_484,c_82]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(X0,ld(X0,rd(X2,X2)))),
inference(demodulation,[status(thm)],[c_188,c_176]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X0),mult(rd(X0,X1),X1)) = mult(X0,mult(X0,ld(X0,rd(X1,X1)))),
inference(superposition,[status(thm)],[c_593,c_185]) ).
tcf(c_630,plain,
( ( mult(sK0,mult(sK0,ld(sK0,rd(sK2,sK2)))) != mult(rd(sK0,sK2),sK2) )
| ( mult(rd(sK0,ld(sK1,sK2)),ld(sK1,sK2)) != mult(rd(sK0,sK2),sK2) ) ),
inference(demodulation,[status(thm)],[c_194,c_617]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X0)) = mult(rd(X0,X0),X0),
inference(superposition,[status(thm)],[c_168,c_214]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_769,c_82]) ).
tcf(c_867,plain,
! [X0: $i] : mult(rd(X0,X0),ld(rd(X0,X0),X0)) = X0,
inference(superposition,[status(thm)],[c_167,c_795]) ).
tcf(c_881,plain,
! [X0: $i] : ld(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_155,c_867]) ).
tcf(c_997,plain,
! [X0: $i,X1: $i] : mult(rd(rd(X0,X0),rd(X1,X0)),rd(X1,X0)) = rd(X0,X0),
inference(superposition,[status(thm)],[c_286,c_486]) ).
tcf(c_1208,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,rd(rd(X1,X0),rd(X1,X0)))) = rd(X0,X0),
inference(demodulation,[status(thm)],[c_997,c_176]) ).
tcf(c_1214,plain,
! [X0: $i] : mult(rd(X0,X0),ld(rd(X0,X0),rd(X0,X0))) = rd(rd(X0,X0),rd(X0,X0)),
inference(superposition,[status(thm)],[c_286,c_1208]) ).
tcf(c_1313,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(ld(X0,X1),X2),ld(ld(ld(X0,X1),X2),X0)) = mult(X0,rd(X0,X0)),
inference(superposition,[status(thm)],[c_795,c_218]) ).
tcf(c_1355,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_1313,c_169]) ).
tcf(c_1465,plain,
! [X0: $i,X1: $i] : mult(rd(mult(X0,X1),X1),X1) = mult(X0,X1),
inference(superposition,[status(thm)],[c_380,c_287]) ).
tcf(c_1479,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,rd(X2,X2))),rd(X1,rd(X2,X2))) = mult(rd(mult(rd(X0,X0),X0),X2),X2),
inference(superposition,[status(thm)],[c_287,c_185]) ).
tcf(c_1489,plain,
! [X0: $i,X1: $i] : mult(mult(rd(X0,X1),X1),X1) = mult(X0,X1),
inference(light_normalisation,[status(thm)],[c_1465,c_55]) ).
tcf(c_1491,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,rd(X2,X2))),rd(X1,rd(X2,X2))) = mult(rd(X0,X2),X2),
inference(light_normalisation,[status(thm)],[c_1479,c_82]) ).
tcf(c_1677,plain,
! [X0: $i,X1: $i] : mult(mult(X0,ld(X0,rd(X1,X1))),X1) = mult(rd(X0,X0),X1),
inference(superposition,[status(thm)],[c_176,c_1489]) ).
tcf(c_1703,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(rd(X0,X0),X2),
inference(demodulation,[status(thm)],[c_214,c_1677]) ).
tcf(c_1705,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),X2) = mult(rd(X0,X0),mult(X1,X2)),
inference(demodulation,[status(thm)],[c_86,c_1703]) ).
tcf(c_1761,plain,
! [X0: $i,X1: $i] : mult(rd(ld(X0,X1),ld(X0,X1)),X0) = X0,
inference(demodulation,[status(thm)],[c_1355,c_1703]) ).
tcf(c_1767,plain,
! [X0: $i,X1: $i] : mult(rd(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),X0) = X0,
inference(superposition,[status(thm)],[c_52,c_1761]) ).
tcf(c_1768,plain,
! [X0: $i] : mult(rd(rd(X0,X0),rd(X0,X0)),X0) = X0,
inference(superposition,[status(thm)],[c_167,c_1761]) ).
tcf(c_1798,plain,
! [X0: $i] : mult(rd(rd(rd(X0,X0),rd(X0,X0)),X0),X0) = rd(X0,X0),
inference(superposition,[status(thm)],[c_1768,c_55]) ).
tcf(c_1959,plain,
! [X0: $i,X1: $i] : mult(rd(mult(X0,mult(X0,ld(X0,X1))),mult(X0,mult(X0,ld(X0,X1)))),X0) = X0,
inference(superposition,[status(thm)],[c_52,c_1767]) ).
tcf(c_1989,plain,
! [X0: $i] : rd(rd(X0,X0),rd(X0,X0)) = rd(X0,X0),
inference(demodulation,[status(thm)],[c_1798,c_176,c_1214]) ).
tcf(c_1998,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X0),ld(rd(X0,X0),rd(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(superposition,[status(thm)],[c_1989,c_176]) ).
tcf(c_2013,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,rd(X2,X2))),rd(X1,rd(X2,X2))) = mult(X0,mult(X0,ld(X0,rd(X2,X2)))),
inference(superposition,[status(thm)],[c_1989,c_593]) ).
tcf(c_2024,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X0),ld(rd(X0,X0),rd(X1,X1))) = mult(X0,ld(X0,rd(X1,X1))),
inference(light_normalisation,[status(thm)],[c_1998,c_176]) ).
tcf(c_2025,plain,
! [X0: $i,X1: $i] : mult(X0,mult(X0,ld(X0,rd(X1,X1)))) = mult(rd(X0,X1),X1),
inference(light_normalisation,[status(thm)],[c_2013,c_1491]) ).
tcf(c_2030,plain,
mult(rd(sK0,ld(sK1,sK2)),ld(sK1,sK2)) != mult(rd(sK0,sK2),sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_630,c_2025]) ).
tcf(c_2031,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_593,c_2025]) ).
tcf(c_2036,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),X2),X2) = mult(X0,mult(rd(X1,X2),X2)),
inference(demodulation,[status(thm)],[c_85,c_2031]) ).
tcf(c_2090,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = mult(rd(X0,X0),X2),
inference(superposition,[status(thm)],[c_52,c_1703]) ).
tcf(c_2091,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X0),ld(rd(X0,X0),X1)) = mult(rd(X0,X0),X1),
inference(superposition,[status(thm)],[c_167,c_1703]) ).
tcf(c_2092,plain,
! [X0: $i,X1: $i] : mult(rd(rd(X0,X0),rd(X0,X0)),X1) = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[c_881,c_1703]) ).
tcf(c_2097,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(rd(X0,X0),X1),mult(rd(X0,X0),X1)),ld(X0,X2)) = ld(X0,X2),
inference(superposition,[status(thm)],[c_1703,c_1767]) ).
tcf(c_2104,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X0),X1) = mult(X0,ld(X0,X1)),
inference(light_normalisation,[status(thm)],[c_2092,c_1989]) ).
tcf(c_2108,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_1703,c_2104]) ).
tcf(c_2172,plain,
! [X0: $i,X1: $i] : mult(rd(rd(X0,X0),X1),X1) = rd(mult(X0,ld(X0,X1)),X1),
inference(superposition,[status(thm)],[c_2104,c_55]) ).
tcf(c_2173,plain,
! [X0: $i,X1: $i] : ld(rd(X0,X0),mult(X0,ld(X0,X1))) = mult(rd(X0,X0),ld(rd(X0,X0),X1)),
inference(superposition,[status(thm)],[c_2104,c_52]) ).
tcf(c_2186,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,rd(X1,X1))) = rd(mult(X0,ld(X0,X1)),X1),
inference(light_normalisation,[status(thm)],[c_2172,c_176]) ).
tcf(c_2187,plain,
! [X0: $i,X1: $i] : ld(rd(X0,X0),mult(X0,ld(X0,X1))) = mult(X0,ld(X0,X1)),
inference(light_normalisation,[status(thm)],[c_2173,c_2091,c_2104]) ).
tcf(c_2248,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
inference(demodulation,[status(thm)],[c_1705,c_2104]) ).
tcf(c_2263,plain,
! [X0: $i,X1: $i] : mult(mult(X0,rd(X0,X0)),X1) = mult(X0,ld(X0,mult(X0,X1))),
inference(superposition,[status(thm)],[c_167,c_2248]) ).
tcf(c_2268,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))) = mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)),
inference(superposition,[status(thm)],[c_2248,c_52]) ).
tcf(c_2279,plain,
! [X0: $i,X1: $i] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,X1),
inference(light_normalisation,[status(thm)],[c_2263,c_52,c_169]) ).
tcf(c_2282,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))) = mult(rd(X0,X0),X2),
inference(light_normalisation,[status(thm)],[c_2268,c_2090]) ).
tcf(c_2972,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = mult(X0,rd(X1,X1)),
inference(demodulation,[status(thm)],[c_2025,c_2279]) ).
tcf(c_2973,plain,
mult(rd(sK0,ld(sK1,sK2)),ld(sK1,sK2)) != mult(sK0,rd(sK2,sK2)),
inference(demodulation,[status(thm)],[c_2030,c_2972]) ).
tcf(c_2977,plain,
! [X0: $i,X1: $i] : mult(mult(X0,rd(X1,X1)),X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[c_1489,c_2972]) ).
tcf(c_2978,plain,
! [X0: $i,X1: $i] : mult(X0,rd(X1,X1)) = rd(mult(X0,X1),X1),
inference(demodulation,[status(thm)],[c_55,c_2972]) ).
tcf(c_3028,plain,
! [X0: $i,X1: $i] : mult(mult(X0,rd(X1,X1)),X1) = mult(mult(X0,X1),rd(X1,X1)),
inference(superposition,[status(thm)],[c_2978,c_2972]) ).
tcf(c_3031,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),rd(X1,X1)) = mult(X0,X1),
inference(light_normalisation,[status(thm)],[c_3028,c_2977]) ).
tcf(c_3077,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),ld(mult(X0,X1),rd(X1,X1))) = ld(mult(X0,X1),mult(X0,X1)),
inference(superposition,[status(thm)],[c_3031,c_52]) ).
tcf(c_3107,plain,
mult(sK0,rd(ld(sK1,sK2),ld(sK1,sK2))) != mult(sK0,rd(sK2,sK2)),
inference(demodulation,[status(thm)],[c_2973,c_2972]) ).
tcf(c_3184,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),rd(X2,X2)) = mult(X0,mult(X1,rd(X2,X2))),
inference(demodulation,[status(thm)],[c_2036,c_2972]) ).
tcf(c_3207,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X0,mult(X1,rd(X2,X2)))) = mult(X0,mult(ld(X0,X1),rd(X2,X2))),
inference(superposition,[status(thm)],[c_3184,c_2248]) ).
tcf(c_3346,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),rd(X2,X2))) = rd(mult(X0,ld(X0,X2)),X2),
inference(superposition,[status(thm)],[c_2108,c_2186]) ).
tcf(c_3621,plain,
! [X0: $i,X1: $i] : ld(rd(X0,X0),mult(X0,mult(X0,ld(X0,X1)))) = mult(X0,mult(X0,ld(X0,X1))),
inference(superposition,[status(thm)],[c_52,c_2187]) ).
tcf(c_3634,plain,
! [X0: $i,X1: $i] : ld(rd(X0,X0),mult(X0,X1)) = mult(X0,X1),
inference(light_normalisation,[status(thm)],[c_3621,c_2279]) ).
tcf(c_7415,plain,
! [X0: $i,X1: $i] : mult(rd(mult(X0,X1),mult(X0,X1)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1959,c_2279]) ).
tcf(c_7416,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),ld(mult(X0,X1),X0)) = X0,
inference(demodulation,[status(thm)],[c_7415,c_2104]) ).
tcf(c_7486,plain,
! [X0: $i,X1: $i] : ld(rd(mult(X0,X1),mult(X0,X1)),X0) = X0,
inference(superposition,[status(thm)],[c_7416,c_3634]) ).
tcf(c_7493,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_7416,c_2248]) ).
tcf(c_7710,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),mult(X0,X1)),ld(rd(mult(X0,X1),mult(X0,X1)),X2)) = mult(X0,ld(X0,X2)),
inference(superposition,[status(thm)],[c_7486,c_2108]) ).
tcf(c_8222,plain,
! [X0: $i,X1: $i,X2: $i] : ld(rd(mult(X0,X1),mult(X0,X1)),mult(X0,X2)) = mult(X0,X2),
inference(superposition,[status(thm)],[c_7493,c_3634]) ).
tcf(c_8329,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))) = mult(X0,ld(X0,X2)),
inference(demodulation,[status(thm)],[c_2282,c_2104]) ).
tcf(c_8377,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))) = mult(X0,ld(X0,mult(X1,ld(X1,X2)))),
inference(superposition,[status(thm)],[c_2279,c_8329]) ).
tcf(c_8418,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,ld(X0,mult(X1,ld(X1,X2)))) = mult(X0,ld(X0,X2)),
inference(light_normalisation,[status(thm)],[c_8377,c_8329]) ).
tcf(c_10796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(mult(X0,X1),mult(X0,X1)),ld(rd(mult(X0,X1),mult(X0,X1)),X2)) = mult(mult(X0,X3),ld(mult(X0,X3),X2)),
inference(superposition,[status(thm)],[c_8222,c_2108]) ).
tcf(c_10805,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_10796,c_7710]) ).
tcf(c_11153,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,mult(X1,rd(X1,X1)))) = mult(X0,ld(X0,X1)),
inference(superposition,[status(thm)],[c_167,c_8418]) ).
tcf(c_11180,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_8418,c_2279]) ).
tcf(c_11193,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(X1,ld(X1,X2))) = mult(X0,X2),
inference(light_normalisation,[status(thm)],[c_11180,c_2279]) ).
tcf(c_11836,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,rd(X1,X1))) = rd(mult(X0,X1),mult(X0,X1)),
inference(demodulation,[status(thm)],[c_3077,c_167,c_10805]) ).
tcf(c_11840,plain,
! [X0: $i,X1: $i] : ld(mult(X0,ld(X0,rd(X1,X1))),X0) = X0,
inference(demodulation,[status(thm)],[c_7486,c_11836]) ).
tcf(c_11873,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X0),ld(rd(X0,X0),rd(X1,X1))) = rd(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(superposition,[status(thm)],[c_2104,c_11836]) ).
tcf(c_11945,plain,
! [X0: $i,X1: $i] : rd(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))) = mult(X0,ld(X0,rd(X1,X1))),
inference(light_normalisation,[status(thm)],[c_11873,c_2024]) ).
tcf(c_12223,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(X0,ld(X0,rd(X1,X1))),ld(X0,X2)) = ld(X0,X2),
inference(superposition,[status(thm)],[c_2108,c_11840]) ).
tcf(c_13142,plain,
! [X0: $i,X1: $i] : mult(X0,mult(ld(X0,X1),rd(X1,X1))) = mult(X0,ld(X0,X1)),
inference(demodulation,[status(thm)],[c_11153,c_3207]) ).
tcf(c_13168,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,mult(ld(X0,X1),rd(X1,X1)))) = ld(X0,mult(X0,ld(X0,X1))),
inference(superposition,[status(thm)],[c_13142,c_52]) ).
tcf(c_13583,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,rd(X1,X1))),ld(X0,X2)) = mult(X0,ld(X0,ld(X0,X2))),
inference(superposition,[status(thm)],[c_12223,c_10805]) ).
tcf(c_16396,plain,
! [X0: $i,X1: $i] : mult(X0,mult(ld(X0,ld(X0,X1)),rd(X1,X1))) = mult(X0,ld(X0,ld(X0,X1))),
inference(demodulation,[status(thm)],[c_13168,c_52,c_3207]) ).
tcf(c_16627,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,ld(X0,X1))) = ld(X0,X1),
inference(light_normalisation,[status(thm)],[c_2097,c_2104,c_11945,c_13583]) ).
tcf(c_16628,plain,
! [X0: $i,X1: $i] : mult(X0,mult(ld(X0,ld(X0,X1)),rd(X1,X1))) = ld(X0,X1),
inference(demodulation,[status(thm)],[c_16396,c_16627]) ).
tcf(c_16665,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(X0,ld(X0,X1)),rd(X2,X2))) = mult(ld(X0,X1),rd(X2,X2)),
inference(superposition,[status(thm)],[c_16627,c_3184]) ).
tcf(c_16723,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),rd(X1,X1)) = ld(X0,X1),
inference(demodulation,[status(thm)],[c_16628,c_16665]) ).
tcf(c_16747,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),rd(X1,X1))) = ld(ld(X0,X1),ld(X0,X1)),
inference(superposition,[status(thm)],[c_16723,c_52]) ).
tcf(c_16901,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,rd(X1,X1))) = rd(ld(X0,X1),ld(X0,X1)),
inference(demodulation,[status(thm)],[c_16747,c_167,c_2186,c_3346]) ).
tcf(c_16902,plain,
mult(sK0,mult(sK1,ld(sK1,rd(sK2,sK2)))) != mult(sK0,rd(sK2,sK2)),
inference(demodulation,[status(thm)],[c_3107,c_16901]) ).
tcf(c_16904,plain,
$false,
inference(ground_joinability,[status(thm)],[c_16902,c_11193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP685+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 15:47:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 10.30/2.75 % SZS status Started for theBenchmark.p
% 10.30/2.75 % SZS status Theorem for theBenchmark.p
% 10.30/2.75
% 10.30/2.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.30/2.75
% 10.30/2.75 % ------ iProver source info
% 10.30/2.75
% 10.30/2.75 % git: date: 2026-07-19 20:42:38 +0200
% 10.30/2.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.30/2.75 % git: non_committed_changes: false
% 10.30/2.75
% 10.30/2.75 % ------ Parsing...
% 10.30/2.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.30/2.75
% 10.30/2.75 % ------ Preprocessing... sup_sim: 6 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.30/2.75
% 10.30/2.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.30/2.75
% 10.30/2.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.30/2.75 % ------ Proving...
% 10.30/2.75 % ------ Problem Properties
% 10.30/2.75
% 10.30/2.75 %
% 10.30/2.75 % clauses 8
% 10.30/2.75 % conjectures 0
% 10.30/2.75 % EPR 0
% 10.30/2.75 % Horn 8
% 10.30/2.75 % unary 7
% 10.30/2.75 % binary 1
% 10.30/2.75 % lits 9
% 10.30/2.75 % lits eq 9
% 10.30/2.75 % fd_pure 0
% 10.30/2.75 % fd_pseudo 0
% 10.30/2.75 % fd_cond 0
% 10.30/2.75 % fd_pseudo_cond 0
% 10.30/2.75 % AC symbols 0
% 10.30/2.75
% 10.30/2.75 % ------ Schedule dynamic 5 is on
% 10.30/2.75
% 10.30/2.75 % ------ no conjectures: strip conj schedule
% 10.30/2.75
% 10.30/2.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 10.30/2.75
% 10.30/2.75
% 10.30/2.75 % ------
% 10.30/2.75 % Current options:
% 10.30/2.75 % ------
% 10.30/2.75
% 10.30/2.75
% 10.30/2.75 %
% 10.30/2.75
% 10.30/2.75 % ------ Proving...
% 10.30/2.75 %
% 10.30/2.75
% 10.30/2.75 % SZS status Theorem for theBenchmark.p
% 10.30/2.75
% 10.30/2.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.30/2.75
% 10.30/2.75
%------------------------------------------------------------------------------