%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP683+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Thu Sep 24 12:35:07 PM UTC 2026
% Result : Theorem 0.12s 0.61s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 8
% Syntax : Number of formulae : 210 ( 200 unt; 0 def)
% Number of atoms : 220 ( 219 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 19 ~; 8 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 524 ( 515 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : ld(A,mult(A,A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : rd(mult(A,A),A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [D,C,B,A] : ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [D,C,B,A] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [X3,X4,X5] :
( mult(rd(mult(X3,X4),X4),X5) = mult(X3,X5)
& mult(X3,ld(X4,mult(X4,X5))) = mult(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [X3,X4,X5] :
( mult(rd(mult(X3,X4),X4),X5) = mult(X3,X5)
& mult(X3,ld(X4,mult(X4,X5))) = mult(X3,X5) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [X0] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
? [X3,X4,X5] :
( mult(rd(mult(X3,X4),X4),X5) != mult(X3,X5)
| mult(X3,ld(X4,mult(X4,X5))) != mult(X3,X5) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f18,plain,
( ? [X3,X4,X5] : mult(rd(mult(X3,X4),X4),X5) != mult(X3,X5)
| ? [X3,X4,X5] : mult(X3,ld(X4,mult(X4,X5))) != mult(X3,X5) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( mult(rd(mult(sK3_skl,sK4_skl),sK4_skl),sK5_skl) != mult(sK3_skl,sK5_skl)
| mult(sK0_skl,ld(sK1_skl,mult(sK1_skl,sK2_skl))) != mult(sK0_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X3,sK0_skl),skolemize(X4,sK1_skl),skolemize(X5,sK2_skl),skolemize(X3,sK3_skl),skolemize(X4,sK4_skl),skolemize(X5,sK5_skl)],[f18]) ).
fof(f20,plain,
( mult(rd(mult(sK3_skl,sK4_skl),sK4_skl),sK5_skl) != mult(sK3_skl,sK5_skl)
| mult(sK0_skl,ld(sK1_skl,mult(sK1_skl,sK2_skl))) != mult(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] : mult(X0,ld(X0,X0)) = X0,
inference(backward_demodulation,[status(thm)],[f12,f10]) ).
fof(f22,plain,
! [X0] : mult(rd(X0,X0),X0) = X0,
inference(backward_demodulation,[status(thm)],[f13,f11]) ).
fof(f23,plain,
! [X0,X1,X2,X3] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f12,f14]) ).
fof(f24,plain,
! [X0,X1,X2,X3] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f12,f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(forward_demodulation,[status(thm)],[f13,f15]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(forward_demodulation,[status(thm)],[f13,f25]) ).
fof(f27,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(forward_demodulation,[status(thm)],[f12,f16]) ).
fof(f28,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(forward_demodulation,[status(thm)],[f13,f27]) ).
fof(f29,plain,
( mult(rd(mult(sK3_skl,sK4_skl),sK4_skl),sK5_skl) != mult(sK3_skl,sK5_skl)
| mult(sK0_skl,mult(sK1_skl,ld(sK1_skl,sK2_skl))) != mult(sK0_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f12,f20]) ).
fof(f30,plain,
( mult(mult(rd(sK3_skl,sK4_skl),sK4_skl),sK5_skl) != mult(sK3_skl,sK5_skl)
| mult(sK0_skl,mult(sK1_skl,ld(sK1_skl,sK2_skl))) != mult(sK0_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f13,f29]) ).
fof(f31,plain,
! [X0] : mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(paramodulation,[status(thm)],[f21,f12]) ).
fof(f33,plain,
! [X0] : mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(paramodulation,[status(thm)],[f22,f13]) ).
fof(f34,plain,
! [X0] : mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(paramodulation,[status(thm)],[f21,f13]) ).
fof(f35,plain,
! [X0] : mult(X0,ld(X0,ld(X0,X0))) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f28,f33]) ).
fof(f36,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(backward_demodulation,[status(thm)],[f39,f22]) ).
fof(f38,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(ld(X0,X0),X1),X1),
inference(backward_demodulation,[status(thm)],[f39,f28]) ).
fof(f39,plain,
! [X0] : ld(X0,X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f31,f35]) ).
fof(f46,plain,
! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f12,f24]) ).
fof(f50,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(mult(X0,ld(X0,ld(X2,X2))),X2),
inference(paramodulation,[status(thm)],[f36,f24]) ).
fof(f54,plain,
! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f12,f46]) ).
fof(f57,plain,
! [X0,X1,X2] : mult(mult(rd(X0,rd(X1,X2)),rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(rd(X1,X2),X2),X2)),
inference(paramodulation,[status(thm)],[f13,f26]) ).
fof(f60,plain,
! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(ld(X0,X0),mult(rd(X0,X2),X2)),
inference(paramodulation,[status(thm)],[f36,f26]) ).
fof(f61,plain,
! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
inference(paramodulation,[status(thm)],[f21,f26]) ).
fof(f62,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),mult(rd(X2,X3),X3)),rd(mult(X2,X3),X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(paramodulation,[status(thm)],[f13,f26]) ).
fof(f71,plain,
! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(X0,ld(X0,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f38,f61]) ).
fof(f72,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),mult(rd(X2,X3),X3)),mult(rd(X2,X3),X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(forward_demodulation,[status(thm)],[f13,f62]) ).
fof(f96,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = mult(ld(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f39,f38]) ).
fof(f98,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,ld(X0,ld(X1,X1))),rd(X2,X3)),rd(X2,X3)) = mult(rd(ld(X0,X0),X1),mult(rd(X1,X3),X3)),
inference(paramodulation,[status(thm)],[f38,f26]) ).
fof(f100,plain,
! [X0,X1] : mult(rd(rd(ld(X0,X0),X1),X1),X1) = rd(mult(X0,ld(X0,ld(X1,X1))),X1),
inference(paramodulation,[status(thm)],[f38,f13]) ).
fof(f102,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f36,f96]) ).
fof(f103,plain,
! [X0,X1,X2] : mult(X0,mult(rd(ld(X0,ld(X1,X1)),X2),X2)) = mult(rd(ld(X0,X0),X1),mult(rd(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f26,f98]) ).
fof(f121,plain,
! [X0,X1,X2] : mult(X0,ld(mult(X0,ld(X0,X0)),mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f21,f54]) ).
fof(f131,plain,
! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,mult(X0,X1))),ld(mult(X0,mult(X0,ld(X0,X1))),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f12,f54]) ).
fof(f138,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = mult(mult(X0,ld(X0,ld(X2,X2))),X2),
inference(paramodulation,[status(thm)],[f36,f54]) ).
fof(f147,plain,
! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
inference(paramodulation,[status(thm)],[f54,f12]) ).
fof(f164,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(ld(X2,X2),X2))),
inference(backward_demodulation,[status(thm)],[f173,f50]) ).
fof(f173,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f21,f121]) ).
fof(f217,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,mult(mult(X0,X1),ld(mult(X0,mult(X0,ld(X0,X1))),mult(X2,X3))))) = mult(mult(X0,ld(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f173,f131]) ).
fof(f218,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,mult(mult(X0,X1),ld(mult(X0,mult(X0,ld(X0,X1))),mult(X2,X3))))) = mult(X0,ld(X0,mult(X2,X3))),
inference(forward_demodulation,[status(thm)],[f173,f217]) ).
fof(f241,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(mult(X0,ld(X0,ld(X2,X2))),X2),
inference(forward_demodulation,[status(thm)],[f173,f138]) ).
fof(f242,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(X0,ld(X0,mult(ld(X2,X2),X2))),
inference(forward_demodulation,[status(thm)],[f173,f241]) ).
fof(f246,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(X0,ld(X0,X2)),
inference(forward_demodulation,[status(thm)],[f36,f242]) ).
fof(f271,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3)))))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
inference(forward_demodulation,[status(thm)],[f173,f147]) ).
fof(f272,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
inference(forward_demodulation,[status(thm)],[f246,f271]) ).
fof(f273,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f173,f272]) ).
fof(f297,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(forward_demodulation,[status(thm)],[f36,f164]) ).
fof(f322,plain,
! [X0,X1] : mult(mult(rd(X0,ld(X1,X1)),rd(X1,X1)),rd(X1,X1)) = mult(X0,mult(rd(rd(X1,X1),X1),X1)),
inference(paramodulation,[status(thm)],[f39,f57]) ).
fof(f340,plain,
! [X0,X1] : mult(mult(rd(X0,ld(X1,X1)),ld(X1,X1)),rd(X1,X1)) = mult(X0,mult(rd(rd(X1,X1),X1),X1)),
inference(forward_demodulation,[status(thm)],[f39,f322]) ).
fof(f341,plain,
! [X0,X1] : mult(mult(rd(X0,ld(X1,X1)),ld(X1,X1)),ld(X1,X1)) = mult(X0,mult(rd(rd(X1,X1),X1),X1)),
inference(forward_demodulation,[status(thm)],[f39,f340]) ).
fof(f342,plain,
! [X0,X1] : mult(mult(rd(X0,ld(X1,X1)),ld(X1,X1)),ld(X1,X1)) = mult(X0,mult(rd(ld(X1,X1),X1),X1)),
inference(forward_demodulation,[status(thm)],[f39,f341]) ).
fof(f343,plain,
! [X0,X1] : mult(mult(rd(X0,ld(X1,X1)),ld(X1,X1)),ld(X1,X1)) = mult(X0,mult(X1,ld(X1,ld(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f38,f342]) ).
fof(f344,plain,
! [X0,X1] : mult(mult(rd(X0,ld(X1,X1)),ld(X1,X1)),ld(X1,X1)) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f31,f343]) ).
fof(f415,plain,
! [X0,X1] : mult(X0,ld(X0,mult(X0,X1))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f21,f173]) ).
fof(f417,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(mult(X0,X1),X2))) = mult(mult(X0,mult(X0,ld(X0,X1))),X2),
inference(paramodulation,[status(thm)],[f12,f173]) ).
fof(f425,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
inference(paramodulation,[status(thm)],[f173,f12]) ).
fof(f436,plain,
! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(X2,X2)),
inference(backward_demodulation,[status(thm)],[f439,f71]) ).
fof(f437,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,mult(mult(X0,X1),ld(mult(X0,X1),mult(X2,X3))))) = mult(X0,ld(X0,mult(X2,X3))),
inference(backward_demodulation,[status(thm)],[f439,f218]) ).
fof(f439,plain,
! [X0,X1] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f12,f415]) ).
fof(f443,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(mult(X0,X1),X2))) = mult(mult(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f439,f417]) ).
fof(f456,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f173,f425]) ).
fof(f457,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,ld(X0,X2)),mult(X0,ld(X0,mult(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f246,f456]) ).
fof(f458,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = mult(X0,ld(X0,ld(mult(X0,ld(X0,X2)),mult(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f273,f457]) ).
fof(f459,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(rd(X1,X2),X2)),
inference(backward_demodulation,[status(thm)],[f436,f26]) ).
fof(f468,plain,
! [X0,X1] : mult(X0,ld(X1,X1)) = mult(ld(X0,X0),mult(rd(X0,X1),X1)),
inference(backward_demodulation,[status(thm)],[f436,f60]) ).
fof(f469,plain,
! [X0,X1,X2,X3] : mult(mult(X0,X1),ld(mult(X0,X1),mult(X2,X3))) = mult(X0,ld(X0,mult(X2,X3))),
inference(forward_demodulation,[status(thm)],[f443,f437]) ).
fof(f472,plain,
! [X0,X1] : mult(rd(X0,ld(X1,X1)),mult(rd(ld(X1,X1),X1),X1)) = mult(X0,ld(X1,X1)),
inference(backward_demodulation,[status(thm)],[f459,f344]) ).
fof(f477,plain,
! [X0,X1] : mult(rd(X0,ld(X1,X1)),mult(X1,ld(X1,ld(X1,X1)))) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f38,f472]) ).
fof(f478,plain,
! [X0] : mult(X0,ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(backward_demodulation,[status(thm)],[f481,f34]) ).
fof(f481,plain,
! [X0,X1] : mult(rd(X0,ld(X1,X1)),ld(X1,X1)) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f31,f477]) ).
fof(f488,plain,
! [X0] : X0 = rd(X0,ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f21,f478]) ).
fof(f514,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(mult(X0,X1),ld(X2,X2))) = ld(mult(X0,X1),mult(X0,mult(rd(X1,X2),X2))),
inference(paramodulation,[status(thm)],[f459,f12]) ).
fof(f605,plain,
! [X0,X1,X2] : mult(rd(X0,mult(rd(X1,X2),X2)),mult(rd(X1,X2),X2)) = mult(ld(X0,X0),mult(rd(X0,X2),X2)),
inference(paramodulation,[status(thm)],[f36,f72]) ).
fof(f622,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),mult(rd(X2,ld(X2,X2)),ld(X2,X2))),mult(X2,ld(X2,X2))) = mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))),
inference(paramodulation,[status(thm)],[f488,f72]) ).
fof(f623,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),mult(rd(X2,X2),X2)),mult(ld(X2,X2),X2)) = mult(X0,mult(rd(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f39,f72]) ).
fof(f637,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(rd(X1,X2),X2)),
inference(backward_demodulation,[status(thm)],[f640,f72]) ).
fof(f640,plain,
! [X0,X1,X2] : mult(rd(X0,mult(rd(X1,X2),X2)),mult(rd(X1,X2),X2)) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f468,f605]) ).
fof(f680,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),mult(X2,ld(X2,X2))),mult(X2,ld(X2,X2))) = mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f481,f622]) ).
fof(f681,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),X2),mult(X2,ld(X2,X2))) = mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f21,f680]) ).
fof(f682,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),X2),X2) = mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f21,f681]) ).
fof(f708,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),X2),X2) = mult(X0,mult(X1,ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f481,f682]) ).
fof(f709,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),mult(ld(X2,X2),X2)),mult(ld(X2,X2),X2)) = mult(X0,mult(rd(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f39,f623]) ).
fof(f710,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(mult(ld(X2,X2),X2),mult(ld(X2,X2),X2)))) = mult(X0,mult(rd(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f708,f709]) ).
fof(f711,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X2,mult(ld(X2,X2),X2)))) = mult(X0,mult(rd(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f36,f710]) ).
fof(f717,plain,
! [X0,X1,X2] : mult(X0,mult(rd(ld(X0,ld(X1,X1)),X2),X2)) = mult(rd(ld(X0,X0),X1),mult(X1,ld(X2,X2))),
inference(backward_demodulation,[status(thm)],[f734,f103]) ).
fof(f730,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(mult(X0,X1),ld(X2,X2))) = ld(mult(X0,X1),mult(X0,mult(X1,ld(X2,X2)))),
inference(backward_demodulation,[status(thm)],[f734,f514]) ).
fof(f734,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X2,X2))) = mult(X0,mult(rd(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f36,f711]) ).
fof(f746,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(X1,ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f734,f637]) ).
fof(f795,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X0,ld(X1,X1)),ld(X2,X2))) = mult(rd(ld(X0,X0),X1),mult(X1,ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f734,f717]) ).
fof(f800,plain,
! [X0] : mult(rd(rd(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),ld(X0,X0)) = rd(ld(X0,X0),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f102,f100]) ).
fof(f806,plain,
! [X0] : mult(rd(ld(X0,X0),ld(X0,X0)),ld(X0,X0)) = rd(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f481,f800]) ).
fof(f807,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = rd(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f38,f806]) ).
fof(f808,plain,
! [X0] : ld(X0,X0) = rd(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f102,f807]) ).
fof(f822,plain,
! [X0] : ld(X0,X0) = ld(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f39,f808]) ).
fof(f836,plain,
! [X0,X1] : mult(rd(rd(ld(X0,X0),ld(X1,X1)),ld(X1,X1)),ld(X1,X1)) = rd(mult(X0,ld(X0,ld(X1,X1))),ld(X1,X1)),
inference(paramodulation,[status(thm)],[f822,f100]) ).
fof(f851,plain,
! [X0,X1] : mult(rd(ld(X0,X0),ld(X1,X1)),ld(X1,X1)) = rd(mult(X0,ld(X0,ld(X1,X1))),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f481,f836]) ).
fof(f852,plain,
! [X0,X1] : mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))) = rd(mult(X0,ld(X0,ld(X1,X1))),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f38,f851]) ).
fof(f853,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = rd(mult(X0,ld(X0,ld(X1,X1))),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f822,f852]) ).
fof(f880,plain,
! [X0,X1] : ld(X0,X1) = mult(X0,ld(X0,ld(X0,X1))),
inference(paramodulation,[status(thm)],[f21,f297]) ).
fof(f893,plain,
! [X0,X1,X2] : mult(ld(X0,X1),mult(X0,ld(X0,X2))) = mult(ld(X0,X1),X2),
inference(paramodulation,[status(thm)],[f297,f439]) ).
fof(f897,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),ld(ld(X0,X1),X2))) = ld(ld(X0,X1),mult(X0,ld(X0,X2))),
inference(paramodulation,[status(thm)],[f297,f12]) ).
fof(f917,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(ld(X0,X1),X2))) = ld(ld(X0,X1),mult(X0,ld(X0,X2))),
inference(forward_demodulation,[status(thm)],[f297,f897]) ).
fof(f918,plain,
! [X0,X1,X2] : ld(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2))))),
inference(paramodulation,[status(thm)],[f173,f880]) ).
fof(f919,plain,
! [X0,X1,X2] : ld(ld(X0,X1),X2) = mult(X0,ld(X0,ld(ld(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f297,f880]) ).
fof(f932,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,ld(X0,X2)),mult(X2,X1)),
inference(backward_demodulation,[status(thm)],[f934,f458]) ).
fof(f934,plain,
! [X0,X1,X2] : ld(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),X2))),
inference(forward_demodulation,[status(thm)],[f246,f918]) ).
fof(f937,plain,
! [X0,X1,X2] : ld(ld(X0,X1),X2) = ld(ld(X0,X1),mult(X0,ld(X0,X2))),
inference(backward_demodulation,[status(thm)],[f919,f917]) ).
fof(f1012,plain,
! [X0,X1] : mult(ld(rd(X0,X1),rd(X0,X1)),rd(X0,X1)) = mult(rd(X0,X1),ld(X1,X1)),
inference(paramodulation,[status(thm)],[f39,f436]) ).
fof(f1015,plain,
! [X0,X1] : mult(rd(X0,X1),rd(X1,ld(X1,X1))) = mult(X0,ld(ld(X1,X1),ld(X1,X1))),
inference(paramodulation,[status(thm)],[f488,f436]) ).
fof(f1018,plain,
! [X0,X1,X2] : mult(rd(X0,rd(mult(X1,X2),X2)),mult(rd(X1,X2),X2)) = mult(X0,ld(X2,X2)),
inference(paramodulation,[status(thm)],[f13,f436]) ).
fof(f1036,plain,
! [X0,X1] : rd(X0,X1) = mult(rd(X0,X1),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f36,f1012]) ).
fof(f1041,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(ld(X1,X1),ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f488,f1015]) ).
fof(f1043,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(ld(X0,X0),ld(X1,X1)),
inference(backward_demodulation,[status(thm)],[f1067,f38]) ).
fof(f1044,plain,
( mult(mult(sK3_skl,ld(sK4_skl,sK4_skl)),sK5_skl) != mult(sK3_skl,sK5_skl)
| mult(sK0_skl,mult(sK1_skl,ld(sK1_skl,sK2_skl))) != mult(sK0_skl,sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f1067,f30]) ).
fof(f1046,plain,
! [X0,X1] : mult(X0,ld(X1,X1)) = rd(mult(X0,X1),X1),
inference(backward_demodulation,[status(thm)],[f1067,f13]) ).
fof(f1067,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f822,f1041]) ).
fof(f1072,plain,
! [X0,X1,X2] : mult(rd(X0,rd(mult(X1,X2),X2)),mult(X1,ld(X2,X2))) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f734,f1018]) ).
fof(f1073,plain,
! [X0,X1,X2] : mult(rd(X0,mult(rd(X1,X2),X2)),mult(X1,ld(X2,X2))) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f13,f1072]) ).
fof(f1074,plain,
! [X0,X1,X2] : mult(rd(X0,mult(X1,ld(X2,X2))),mult(X1,ld(X2,X2))) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f1067,f1073]) ).
fof(f1075,plain,
! [X0,X1,X2] : mult(X0,ld(mult(X1,ld(X2,X2)),mult(X1,ld(X2,X2)))) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f1067,f1074]) ).
fof(f1133,plain,
! [X0,X1] : mult(ld(X0,X0),ld(ld(X0,X0),ld(X1,X1))) = ld(ld(X0,X0),mult(X0,ld(X0,ld(X1,X1)))),
inference(paramodulation,[status(thm)],[f1043,f12]) ).
fof(f1156,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(ld(X0,X0),mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f297,f1133]) ).
fof(f1158,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(ld(X0,X0),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f937,f1156]) ).
fof(f1196,plain,
! [X0,X1] : mult(mult(X0,ld(X1,X1)),X1) = mult(mult(X0,X1),ld(X1,X1)),
inference(paramodulation,[status(thm)],[f1046,f1067]) ).
fof(f1199,plain,
! [X0,X1] : mult(rd(X0,X1),ld(X1,X1)) = rd(mult(X0,ld(X1,X1)),X1),
inference(paramodulation,[status(thm)],[f1067,f1046]) ).
fof(f1202,plain,
! [X0,X1] : mult(mult(X0,ld(X1,X1)),X1) = mult(X0,mult(X1,ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f746,f1196]) ).
fof(f1204,plain,
! [X0,X1] : mult(mult(X0,ld(X1,X1)),X1) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f21,f1202]) ).
fof(f1209,plain,
! [X0,X1] : rd(X0,X1) = rd(mult(X0,ld(X1,X1)),X1),
inference(forward_demodulation,[status(thm)],[f1036,f1199]) ).
fof(f1320,plain,
! [X0,X1] : mult(mult(X0,ld(ld(X1,X1),ld(X1,X1))),X1) = mult(rd(X0,ld(X1,X1)),X1),
inference(paramodulation,[status(thm)],[f1067,f1204]) ).
fof(f1324,plain,
! [X0,X1] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(ld(X0,X0),X1),
inference(paramodulation,[status(thm)],[f1043,f1204]) ).
fof(f1333,plain,
! [X0,X1] : mult(mult(X0,mult(X1,ld(X1,ld(X1,X1)))),X1) = mult(rd(X0,ld(X1,X1)),X1),
inference(forward_demodulation,[status(thm)],[f1158,f1320]) ).
fof(f1334,plain,
! [X0,X1] : mult(mult(X0,ld(X1,X1)),X1) = mult(rd(X0,ld(X1,X1)),X1),
inference(forward_demodulation,[status(thm)],[f880,f1333]) ).
fof(f1335,plain,
! [X0,X1] : mult(X0,X1) = mult(rd(X0,ld(X1,X1)),X1),
inference(forward_demodulation,[status(thm)],[f1204,f1334]) ).
fof(f1342,plain,
! [X0,X1] : mult(X0,ld(X0,mult(ld(X1,X1),X1))) = mult(ld(X0,X0),X1),
inference(forward_demodulation,[status(thm)],[f173,f1324]) ).
fof(f1349,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(ld(X0,X0),X1),
inference(forward_demodulation,[status(thm)],[f36,f1342]) ).
fof(f1425,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X1,X1)),ld(X2,X2)) = mult(rd(X0,X1),mult(X1,ld(X2,X2))),
inference(paramodulation,[status(thm)],[f1067,f746]) ).
fof(f1438,plain,
! [X0,X1,X2] : mult(mult(X0,mult(X1,ld(X2,X2))),X2) = mult(mult(X0,X1),X2),
inference(paramodulation,[status(thm)],[f746,f1204]) ).
fof(f1450,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X1,X1),ld(X2,X2))) = mult(rd(X0,X1),mult(X1,ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f746,f1425]) ).
fof(f1459,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X0,ld(X1,X1)),ld(X2,X2))) = mult(ld(X0,X0),mult(X1,ld(X1,ld(X2,X2)))),
inference(backward_demodulation,[status(thm)],[f1466,f795]) ).
fof(f1466,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X1,ld(X2,X2)))) = mult(rd(X0,X1),mult(X1,ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f1349,f1450]) ).
fof(f1503,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X0,ld(X1,X1)),ld(X2,X2))) = mult(X0,ld(X0,mult(X1,ld(X1,ld(X2,X2))))),
inference(forward_demodulation,[status(thm)],[f1349,f1459]) ).
fof(f1520,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),ld(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))) = ld(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),mult(X0,mult(X1,ld(X2,X2)))),
inference(paramodulation,[status(thm)],[f1335,f730]) ).
fof(f1527,plain,
! [X0,X1] : mult(mult(X0,X1),ld(mult(X0,X1),ld(X1,X1))) = ld(mult(X0,X1),mult(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f730]) ).
fof(f1591,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,mult(X2,ld(X2,ld(X2,X2))))),ld(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))) = ld(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),mult(X0,mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f1158,f1520]) ).
fof(f1592,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,ld(X2,X2))),ld(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),ld(X2,X2))) = ld(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),mult(X0,mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f880,f1591]) ).
fof(f1593,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,ld(X2,X2))),ld(mult(X0,rd(X1,mult(X2,ld(X2,ld(X2,X2))))),ld(X2,X2))) = ld(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),mult(X0,mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f1158,f1592]) ).
fof(f1594,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,ld(X2,X2))),ld(mult(X0,rd(X1,ld(X2,X2))),ld(X2,X2))) = ld(mult(X0,rd(X1,ld(ld(X2,X2),ld(X2,X2)))),mult(X0,mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f880,f1593]) ).
fof(f1595,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,ld(X2,X2))),ld(mult(X0,rd(X1,ld(X2,X2))),ld(X2,X2))) = ld(mult(X0,rd(X1,mult(X2,ld(X2,ld(X2,X2))))),mult(X0,mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f1158,f1594]) ).
fof(f1596,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,ld(X2,X2))),ld(mult(X0,rd(X1,ld(X2,X2))),ld(X2,X2))) = ld(mult(X0,rd(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f880,f1595]) ).
fof(f1624,plain,
! [X0,X1] : mult(X0,ld(X0,ld(ld(X0,X0),X1))) = mult(X0,ld(X0,X1)),
inference(paramodulation,[status(thm)],[f297,f1349]) ).
fof(f1643,plain,
! [X0,X1] : mult(ld(X0,X0),ld(X1,X1)) = rd(mult(X0,ld(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f1349,f1046]) ).
fof(f1648,plain,
! [X0,X1] : ld(ld(X0,X0),X1) = mult(X0,ld(X0,X1)),
inference(forward_demodulation,[status(thm)],[f919,f1624]) ).
fof(f1701,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))),
inference(backward_demodulation,[status(thm)],[f1702,f853]) ).
fof(f1702,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = rd(mult(X0,ld(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f1349,f1643]) ).
fof(f1709,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,ld(X0,mult(X1,ld(X1,ld(X1,X1))))),
inference(forward_demodulation,[status(thm)],[f1158,f1701]) ).
fof(f1710,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,mult(ld(X0,ld(X1,X1)),ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f1503,f1709]) ).
fof(f1743,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(mult(X0,X1),ld(ld(X2,X2),ld(X2,X2)))) = ld(mult(X0,X1),mult(X0,mult(X1,mult(X2,ld(X2,ld(X2,X2)))))),
inference(paramodulation,[status(thm)],[f1648,f730]) ).
fof(f1746,plain,
! [X0,X1] : rd(X0,ld(X1,X1)) = rd(mult(X0,mult(X1,ld(X1,ld(X1,X1)))),ld(X1,X1)),
inference(paramodulation,[status(thm)],[f1648,f1209]) ).
fof(f1785,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(mult(X0,X1),mult(X2,ld(X2,ld(X2,X2))))) = ld(mult(X0,X1),mult(X0,mult(X1,mult(X2,ld(X2,ld(X2,X2)))))),
inference(forward_demodulation,[status(thm)],[f1648,f1743]) ).
fof(f1786,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(X1,ld(X1,X1))))) = ld(mult(X0,X2),mult(X0,mult(X2,mult(X1,ld(X1,ld(X1,X1)))))),
inference(forward_demodulation,[status(thm)],[f469,f1785]) ).
fof(f1787,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X0,ld(X1,X1)),ld(X1,X1))) = ld(mult(X0,X2),mult(X0,mult(X2,mult(X1,ld(X1,ld(X1,X1)))))),
inference(forward_demodulation,[status(thm)],[f1503,f1786]) ).
fof(f1788,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,X2),mult(X0,mult(X2,mult(X1,ld(X1,ld(X1,X1)))))),
inference(forward_demodulation,[status(thm)],[f1710,f1787]) ).
fof(f1789,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(mult(X0,X1),ld(X2,X2))) = mult(X0,ld(X0,ld(X2,X2))),
inference(backward_demodulation,[status(thm)],[f1790,f730]) ).
fof(f1790,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,X2),mult(X0,mult(X2,ld(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f880,f1788]) ).
fof(f1797,plain,
! [X0,X1] : rd(X0,ld(X1,X1)) = rd(mult(X0,ld(X1,X1)),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f880,f1746]) ).
fof(f1798,plain,
! [X0,X1] : rd(X0,ld(X1,X1)) = mult(X0,ld(ld(X1,X1),ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f1046,f1797]) ).
fof(f1799,plain,
! [X0,X1] : rd(X0,ld(X1,X1)) = mult(X0,mult(X1,ld(X1,ld(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f1648,f1798]) ).
fof(f1808,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,ld(X2,X2))),ld(mult(X0,rd(X1,ld(X2,X2))),ld(X2,X2))) = ld(mult(X0,mult(X1,ld(X2,X2))),mult(X0,mult(X1,ld(X2,X2)))),
inference(backward_demodulation,[status(thm)],[f1812,f1596]) ).
fof(f1812,plain,
! [X0,X1] : rd(X0,ld(X1,X1)) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f880,f1799]) ).
fof(f1875,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,X1),mult(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1789,f1527]) ).
fof(f1894,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,mult(X2,ld(X1,X1))),mult(X0,mult(X2,ld(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f1789,f1808]) ).
fof(f1901,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,ld(X0,ld(mult(X2,ld(X1,X1)),mult(X2,ld(X1,X1))))),
inference(backward_demodulation,[status(thm)],[f1875,f1894]) ).
fof(f1905,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X1,ld(ld(X2,X2),ld(X2,X2))))) = mult(X0,ld(X2,X2)),
inference(backward_demodulation,[status(thm)],[f1875,f1075]) ).
fof(f1907,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,ld(X0,mult(X2,ld(X2,ld(ld(X1,X1),ld(X1,X1)))))),
inference(forward_demodulation,[status(thm)],[f1875,f1901]) ).
fof(f1908,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,mult(ld(X0,ld(X2,X2)),ld(ld(X1,X1),ld(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f1503,f1907]) ).
fof(f1909,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,mult(ld(X0,ld(X2,X2)),mult(X1,ld(X1,ld(X1,X1))))),
inference(forward_demodulation,[status(thm)],[f1648,f1908]) ).
fof(f1916,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = mult(X0,mult(ld(X0,ld(X2,X2)),ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f880,f1909]) ).
fof(f1923,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X1,mult(X2,ld(X2,ld(X2,X2)))))) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f1648,f1905]) ).
fof(f1924,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(ld(X1,ld(X2,X2)),ld(X2,X2)))) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f1503,f1923]) ).
fof(f1938,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X1,ld(X2,X2)))) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f1916,f1924]) ).
fof(f2400,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,mult(X1,ld(X1,X2)))) = ld(mult(X0,ld(X0,ld(X1,X3))),mult(ld(X1,X3),X2)),
inference(paramodulation,[status(thm)],[f893,f932]) ).
fof(f2477,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(X1,X2)))) = mult(X0,ld(X0,X2)),
inference(forward_demodulation,[status(thm)],[f932,f2400]) ).
fof(f3388,plain,
! [X0,X1,X2] : mult(mult(X0,mult(X1,ld(X1,ld(X2,X2)))),X2) = mult(mult(X0,ld(X1,X1)),X2),
inference(paramodulation,[status(thm)],[f1349,f1438]) ).
fof(f3437,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X1,X1)),X1) = mult(mult(X0,ld(X2,X2)),X1),
inference(forward_demodulation,[status(thm)],[f1938,f3388]) ).
fof(f3438,plain,
( mult(sK3_skl,sK5_skl) != mult(sK3_skl,sK5_skl)
| mult(sK0_skl,mult(sK1_skl,ld(sK1_skl,sK2_skl))) != mult(sK0_skl,sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f3451,f1044]) ).
fof(f3451,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(mult(X0,ld(X2,X2)),X1),
inference(forward_demodulation,[status(thm)],[f1204,f3437]) ).
fof(f3487,plain,
mult(sK0_skl,mult(sK1_skl,ld(sK1_skl,sK2_skl))) != mult(sK0_skl,sK2_skl),
inference(trivial_equality_resolution,[status(thm)],[f3438]) ).
fof(f5454,plain,
! [X0,X1,X2] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,mult(X2,ld(X2,X1))),
inference(paramodulation,[status(thm)],[f2477,f439]) ).
fof(f5563,plain,
mult(sK0_skl,sK2_skl) != mult(sK0_skl,sK2_skl),
inference(backward_demodulation,[status(thm)],[f5578,f3487]) ).
fof(f5578,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(X0,mult(X2,ld(X2,X1))),
inference(forward_demodulation,[status(thm)],[f439,f5454]) ).
fof(f5633,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f5563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP683+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.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 : Sun Sep 20 20:32:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.61 % Refutation found
% 0.12/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.05/0.64 % Elapsed time: 0.275643 seconds
% 1.05/0.64 % CPU time: 1.789448 seconds
% 1.05/0.64 % Total memory used: 102.185 MB
% 1.05/0.64 % Net memory used: 99.877 MB
%------------------------------------------------------------------------------