%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP685+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 : n020.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 12:35:08 PM UTC 2026
% Result : Theorem 0.15s 0.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 8
% Syntax : Number of formulae : 146 ( 131 unt; 0 def)
% Number of atoms : 161 ( 160 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 30 ~; 13 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 10 ( 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 : 318 ( 309 !; 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,
! [X6,X7,X8] :
( rd(mult(X6,rd(X7,X8)),rd(X7,X8)) = rd(mult(X6,X8),X8)
& rd(mult(X6,ld(X7,X8)),ld(X7,X8)) = rd(mult(X6,X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [X6,X7,X8] :
( rd(mult(X6,rd(X7,X8)),rd(X7,X8)) = rd(mult(X6,X8),X8)
& rd(mult(X6,ld(X7,X8)),ld(X7,X8)) = rd(mult(X6,X8),X8) ),
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,
? [X6,X7,X8] :
( rd(mult(X6,rd(X7,X8)),rd(X7,X8)) != rd(mult(X6,X8),X8)
| rd(mult(X6,ld(X7,X8)),ld(X7,X8)) != rd(mult(X6,X8),X8) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f18,plain,
( ? [X6,X7,X8] : rd(mult(X6,rd(X7,X8)),rd(X7,X8)) != rd(mult(X6,X8),X8)
| ? [X6,X7,X8] : rd(mult(X6,ld(X7,X8)),ld(X7,X8)) != rd(mult(X6,X8),X8) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( rd(mult(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl)) != rd(mult(sK3_skl,sK5_skl),sK5_skl)
| rd(mult(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != rd(mult(sK0_skl,sK2_skl),sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X6,sK0_skl),skolemize(X7,sK1_skl),skolemize(X8,sK2_skl),skolemize(X6,sK3_skl),skolemize(X7,sK4_skl),skolemize(X8,sK5_skl)],[f18]) ).
fof(f20,plain,
( rd(mult(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl)) != rd(mult(sK3_skl,sK5_skl),sK5_skl)
| rd(mult(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != rd(mult(sK0_skl,sK2_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,
( rd(mult(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl)) != rd(mult(sK3_skl,sK5_skl),sK5_skl)
| mult(rd(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != rd(mult(sK0_skl,sK2_skl),sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f13,f20]) ).
fof(f30,plain,
( rd(mult(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl)) != rd(mult(sK3_skl,sK5_skl),sK5_skl)
| mult(rd(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != mult(rd(sK0_skl,sK2_skl),sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f13,f29]) ).
fof(f31,plain,
( mult(rd(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl)) != rd(mult(sK3_skl,sK5_skl),sK5_skl)
| mult(rd(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != mult(rd(sK0_skl,sK2_skl),sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f13,f30]) ).
fof(f32,plain,
( mult(rd(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl)) != mult(rd(sK3_skl,sK5_skl),sK5_skl)
| mult(rd(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != mult(rd(sK0_skl,sK2_skl),sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f13,f31]) ).
fof(f34,plain,
! [X0] : mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(paramodulation,[status(thm)],[f21,f12]) ).
fof(f35,plain,
! [X0] : mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(paramodulation,[status(thm)],[f22,f13]) ).
fof(f36,plain,
! [X0] : mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(paramodulation,[status(thm)],[f21,f13]) ).
fof(f37,plain,
! [X0] : mult(X0,ld(X0,ld(X0,X0))) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f28,f35]) ).
fof(f38,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(backward_demodulation,[status(thm)],[f41,f22]) ).
fof(f40,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(ld(X0,X0),X1),X1),
inference(backward_demodulation,[status(thm)],[f41,f28]) ).
fof(f41,plain,
! [X0] : ld(X0,X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f34,f37]) ).
fof(f47,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
inference(paramodulation,[status(thm)],[f21,f24]) ).
fof(f55,plain,
! [X0] : mult(ld(X0,X0),ld(ld(X0,X0),X0)) = ld(ld(X0,X0),X0),
inference(paramodulation,[status(thm)],[f38,f12]) ).
fof(f64,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(f68,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)],[f38,f26]) ).
fof(f70,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(f71,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(f81,plain,
( mult(ld(sK3_skl,sK3_skl),mult(rd(sK3_skl,sK5_skl),sK5_skl)) != mult(rd(sK3_skl,sK5_skl),sK5_skl)
| mult(rd(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != mult(rd(sK0_skl,sK2_skl),sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f68,f32]) ).
fof(f83,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)],[f40,f70]) ).
fof(f84,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,f71]) ).
fof(f90,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)],[f41,f40]) ).
fof(f96,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f38,f90]) ).
fof(f109,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),X2)) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
inference(paramodulation,[status(thm)],[f12,f47]) ).
fof(f115,plain,
! [X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),ld(X0,X0))) = mult(ld(X0,X0),ld(ld(X0,X0),ld(X0,X0))),
inference(paramodulation,[status(thm)],[f34,f47]) ).
fof(f116,plain,
! [X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),X0)) = mult(X0,ld(X0,X0)),
inference(paramodulation,[status(thm)],[f21,f47]) ).
fof(f126,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(ld(X0,X2),ld(ld(X0,X2),X1))),
inference(paramodulation,[status(thm)],[f47,f12]) ).
fof(f127,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f12,f109]) ).
fof(f130,plain,
! [X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),ld(X0,X0))) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f21,f115]) ).
fof(f131,plain,
! [X0] : X0 = ld(ld(X0,X0),X0),
inference(backward_demodulation,[status(thm)],[f132,f55]) ).
fof(f132,plain,
! [X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f21,f116]) ).
fof(f159,plain,
! [X0,X1,X2] : mult(ld(ld(X0,X0),X0),ld(X0,mult(X1,X2))) = mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),X2),
inference(paramodulation,[status(thm)],[f131,f24]) ).
fof(f167,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,X2))) = mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f131,f159]) ).
fof(f197,plain,
! [X0] : mult(X0,ld(ld(ld(X0,X0),X0),ld(ld(X0,X0),ld(X0,X0)))) = ld(ld(X0,X0),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f131,f130]) ).
fof(f209,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = ld(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f131,f197]) ).
fof(f212,plain,
! [X0] : ld(X0,X0) = ld(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f96,f209]) ).
fof(f241,plain,
! [X0,X1,X2] : mult(ld(ld(X0,X0),ld(X0,X0)),ld(ld(X0,X0),mult(X1,X2))) = mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),X2),
inference(paramodulation,[status(thm)],[f212,f24]) ).
fof(f275,plain,
! [X0,X1,X2] : mult(ld(X0,X0),ld(ld(X0,X0),mult(X1,X2))) = mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f212,f241]) ).
fof(f276,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),X2) = mult(mult(ld(X0,X0),ld(ld(X0,X0),X1)),X2),
inference(forward_demodulation,[status(thm)],[f24,f275]) ).
fof(f277,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(X2,ld(X2,X2)))),
inference(backward_demodulation,[status(thm)],[f304,f47]) ).
fof(f295,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(X1,X1))))) = ld(mult(X0,ld(X0,X1)),mult(ld(X0,X2),ld(ld(X0,X2),X1))),
inference(backward_demodulation,[status(thm)],[f304,f126]) ).
fof(f297,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
inference(backward_demodulation,[status(thm)],[f304,f127]) ).
fof(f304,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
inference(forward_demodulation,[status(thm)],[f167,f276]) ).
fof(f317,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(forward_demodulation,[status(thm)],[f21,f277]) ).
fof(f339,plain,
! [X0,X1] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(X1,X1))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f317,f295]) ).
fof(f341,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(X0,ld(X0,mult(X2,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f304,f297]) ).
fof(f343,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(backward_demodulation,[status(thm)],[f345,f339]) ).
fof(f345,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)],[f21,f341]) ).
fof(f379,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)],[f41,f64]) ).
fof(f397,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)],[f41,f379]) ).
fof(f398,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)],[f41,f397]) ).
fof(f399,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)],[f41,f398]) ).
fof(f400,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)],[f40,f399]) ).
fof(f401,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)],[f34,f400]) ).
fof(f428,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,ld(X0,mult(X0,X1))),
inference(paramodulation,[status(thm)],[f21,f304]) ).
fof(f449,plain,
! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(X2,X2)),
inference(backward_demodulation,[status(thm)],[f451,f83]) ).
fof(f451,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12,f428]) ).
fof(f470,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(rd(X1,X2),X2)),
inference(backward_demodulation,[status(thm)],[f449,f26]) ).
fof(f476,plain,
! [X0,X1] : mult(X0,ld(X1,X1)) = mult(ld(X0,X0),mult(rd(X0,X1),X1)),
inference(backward_demodulation,[status(thm)],[f449,f68]) ).
fof(f482,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)],[f470,f401]) ).
fof(f485,plain,
( mult(sK3_skl,ld(sK5_skl,sK5_skl)) != mult(rd(sK3_skl,sK5_skl),sK5_skl)
| mult(rd(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != mult(rd(sK0_skl,sK2_skl),sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f476,f81]) ).
fof(f486,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)],[f40,f482]) ).
fof(f487,plain,
! [X0] : mult(X0,ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(backward_demodulation,[status(thm)],[f490,f36]) ).
fof(f490,plain,
! [X0,X1] : mult(rd(X0,ld(X1,X1)),ld(X1,X1)) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f34,f486]) ).
fof(f494,plain,
! [X0] : X0 = rd(X0,ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f21,f487]) ).
fof(f508,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2))))),
inference(paramodulation,[status(thm)],[f304,f451]) ).
fof(f516,plain,
! [X0,X1] : mult(rd(X0,mult(X0,ld(X0,X1))),mult(X0,ld(X0,X1))) = rd(mult(X0,X1),mult(X0,ld(X0,X1))),
inference(paramodulation,[status(thm)],[f451,f13]) ).
fof(f518,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,X2))) = mult(X0,ld(X0,mult(X1,mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2))))),
inference(forward_demodulation,[status(thm)],[f304,f508]) ).
fof(f519,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,X2))) = mult(X0,ld(X0,mult(X1,mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2))))))),
inference(forward_demodulation,[status(thm)],[f304,f518]) ).
fof(f520,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,X2))) = mult(X0,ld(X0,mult(X1,mult(X0,ld(X0,X2))))),
inference(forward_demodulation,[status(thm)],[f345,f519]) ).
fof(f534,plain,
! [X0,X1] : ld(X0,X1) = mult(X0,ld(X0,ld(X0,X1))),
inference(paramodulation,[status(thm)],[f21,f317]) ).
fof(f540,plain,
! [X0,X1,X2] : mult(ld(X0,X1),mult(ld(X0,X1),ld(ld(X0,X1),X2))) = mult(X0,ld(X0,mult(ld(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f12,f317]) ).
fof(f558,plain,
! [X0,X1,X2] : mult(ld(X0,X1),X2) = mult(X0,ld(X0,mult(ld(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f451,f540]) ).
fof(f575,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))),
inference(paramodulation,[status(thm)],[f212,f470]) ).
fof(f596,plain,
! [X0,X1,X2] : mult(X0,mult(rd(X1,X2),X2)) = mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f470,f575]) ).
fof(f603,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),mult(rd(X2,X3),X3)),mult(X2,ld(X3,X3))) = mult(X0,mult(rd(X1,X3),X3)),
inference(backward_demodulation,[status(thm)],[f617,f84]) ).
fof(f617,plain,
! [X0,X1,X2] : mult(X0,mult(rd(X1,X2),X2)) = mult(X0,mult(X1,ld(X2,X2))),
inference(forward_demodulation,[status(thm)],[f490,f596]) ).
fof(f636,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),mult(rd(X2,X3),X3)),mult(X2,ld(X3,X3))) = mult(X0,mult(X1,ld(X3,X3))),
inference(forward_demodulation,[status(thm)],[f617,f603]) ).
fof(f739,plain,
! [X0,X1,X2] : mult(rd(X0,mult(rd(X1,X2),X2)),rd(mult(X1,X2),X2)) = mult(X0,ld(X2,X2)),
inference(paramodulation,[status(thm)],[f13,f449]) ).
fof(f740,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)],[f494,f449]) ).
fof(f753,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)],[f13,f739]) ).
fof(f754,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(X2,X2)) = mult(X0,mult(X1,ld(X2,X2))),
inference(backward_demodulation,[status(thm)],[f756,f636]) ).
fof(f756,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)],[f617,f753]) ).
fof(f757,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(ld(X1,X1),ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f494,f740]) ).
fof(f759,plain,
! [X0,X1,X2] : mult(X0,ld(rd(X1,X2),rd(X1,X2))) = mult(X0,ld(X2,X2)),
inference(backward_demodulation,[status(thm)],[f772,f449]) ).
fof(f761,plain,
( mult(sK3_skl,ld(sK5_skl,sK5_skl)) != mult(sK3_skl,ld(sK5_skl,sK5_skl))
| mult(rd(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl)) != mult(rd(sK0_skl,sK2_skl),sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f772,f485]) ).
fof(f766,plain,
! [X0,X1] : mult(X0,ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1)))) = rd(mult(X0,X1),mult(X0,ld(X0,X1))),
inference(backward_demodulation,[status(thm)],[f772,f516]) ).
fof(f770,plain,
! [X0,X1,X2] : mult(rd(X0,mult(X1,ld(X2,X2))),mult(X1,ld(X2,X2))) = mult(X0,ld(X2,X2)),
inference(backward_demodulation,[status(thm)],[f772,f756]) ).
fof(f772,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f212,f757]) ).
fof(f789,plain,
( mult(sK3_skl,ld(sK5_skl,sK5_skl)) != mult(sK3_skl,ld(sK5_skl,sK5_skl))
| mult(sK0_skl,ld(ld(sK1_skl,sK2_skl),ld(sK1_skl,sK2_skl))) != mult(rd(sK0_skl,sK2_skl),sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f772,f761]) ).
fof(f790,plain,
( mult(sK3_skl,ld(sK5_skl,sK5_skl)) != mult(sK3_skl,ld(sK5_skl,sK5_skl))
| mult(sK0_skl,ld(ld(sK1_skl,sK2_skl),ld(sK1_skl,sK2_skl))) != mult(sK0_skl,ld(sK2_skl,sK2_skl)) ),
inference(forward_demodulation,[status(thm)],[f772,f789]) ).
fof(f791,plain,
mult(sK0_skl,ld(ld(sK1_skl,sK2_skl),ld(sK1_skl,sK2_skl))) != mult(sK0_skl,ld(sK2_skl,sK2_skl)),
inference(trivial_equality_resolution,[status(thm)],[f790]) ).
fof(f799,plain,
! [X0,X1] : mult(X0,mult(X0,ld(X0,ld(X1,X1)))) = rd(mult(X0,X1),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f343,f766]) ).
fof(f800,plain,
! [X0,X1] : mult(X0,ld(X1,X1)) = rd(mult(X0,X1),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f451,f799]) ).
fof(f801,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)],[f772,f770]) ).
fof(f1219,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(X2,X2)))) = mult(X0,mult(ld(X0,X1),ld(X2,X2))),
inference(paramodulation,[status(thm)],[f304,f754]) ).
fof(f1372,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(X2,X2)) = rd(mult(X0,ld(X0,mult(X1,X2))),mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2))),
inference(paramodulation,[status(thm)],[f304,f800]) ).
fof(f1397,plain,
! [X0] : mult(X0,ld(X0,X0)) = rd(mult(X0,X0),X0),
inference(paramodulation,[status(thm)],[f21,f800]) ).
fof(f1402,plain,
! [X0,X1,X2] : mult(X0,ld(rd(mult(X1,X2),mult(X1,ld(X1,X2))),mult(X1,ld(X2,X2)))) = mult(X0,ld(mult(X1,ld(X1,X2)),mult(X1,ld(X1,X2)))),
inference(paramodulation,[status(thm)],[f800,f759]) ).
fof(f1413,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(X2,X2)))) = rd(mult(X0,ld(X0,mult(X1,X2))),mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2))),
inference(forward_demodulation,[status(thm)],[f304,f1372]) ).
fof(f1414,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X0,X1),ld(X2,X2))) = rd(mult(X0,ld(X0,mult(X1,X2))),mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2))),
inference(forward_demodulation,[status(thm)],[f1219,f1413]) ).
fof(f1415,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X0,X1),ld(X2,X2))) = rd(mult(X0,ld(X0,mult(X1,X2))),mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2))))),
inference(forward_demodulation,[status(thm)],[f304,f1414]) ).
fof(f1416,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X0,X1),ld(X2,X2))) = rd(mult(X0,ld(X0,mult(X1,X2))),mult(X0,ld(X0,X2))),
inference(forward_demodulation,[status(thm)],[f345,f1415]) ).
fof(f1476,plain,
! [X0] : X0 = rd(mult(X0,X0),X0),
inference(forward_demodulation,[status(thm)],[f21,f1397]) ).
fof(f1494,plain,
! [X0,X1,X2] : mult(X0,ld(mult(X1,ld(X2,X2)),mult(X1,ld(X2,X2)))) = mult(X0,ld(mult(X1,ld(X1,X2)),mult(X1,ld(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f800,f1402]) ).
fof(f1495,plain,
! [X0,X1,X2] : mult(X0,ld(X1,X1)) = mult(X0,ld(mult(X2,ld(X2,X1)),mult(X2,ld(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f801,f1494]) ).
fof(f1502,plain,
! [X0,X1,X2] : mult(X0,ld(X1,X1)) = mult(X0,mult(X2,ld(X2,ld(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f343,f1495]) ).
fof(f1524,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = rd(mult(X0,ld(X0,mult(X1,mult(X0,ld(X0,X1))))),mult(X0,ld(X0,X1))),
inference(paramodulation,[status(thm)],[f304,f1476]) ).
fof(f1536,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = rd(mult(X0,ld(X0,mult(X1,X1))),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f520,f1524]) ).
fof(f1537,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(X0,mult(ld(X0,X1),ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f1416,f1536]) ).
fof(f2616,plain,
! [X0,X1] : mult(X0,ld(X0,mult(ld(X0,X1),ld(X1,X1)))) = ld(X0,mult(X0,ld(X0,X1))),
inference(paramodulation,[status(thm)],[f1537,f12]) ).
fof(f2702,plain,
! [X0,X1] : mult(ld(X0,X1),ld(X1,X1)) = ld(X0,mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f558,f2616]) ).
fof(f2703,plain,
! [X0,X1] : mult(ld(X0,X1),ld(X1,X1)) = mult(X0,ld(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12,f2702]) ).
fof(f2706,plain,
! [X0,X1] : mult(ld(X0,X1),ld(X1,X1)) = ld(X0,X1),
inference(forward_demodulation,[status(thm)],[f534,f2703]) ).
fof(f2729,plain,
! [X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),ld(X1,X1))) = ld(ld(X0,X1),ld(X0,X1)),
inference(paramodulation,[status(thm)],[f2706,f12]) ).
fof(f2778,plain,
mult(sK0_skl,mult(sK1_skl,ld(sK1_skl,ld(sK2_skl,sK2_skl)))) != mult(sK0_skl,ld(sK2_skl,sK2_skl)),
inference(backward_demodulation,[status(thm)],[f2786,f791]) ).
fof(f2786,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(ld(X0,X1),ld(X0,X1)),
inference(forward_demodulation,[status(thm)],[f317,f2729]) ).
fof(f2787,plain,
mult(sK0_skl,ld(sK2_skl,sK2_skl)) != mult(sK0_skl,ld(sK2_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f1502,f2778]) ).
fof(f2788,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2787]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP685+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.45 % Computer : n020.cluster.edu
% 0.15/0.45 % Model : x86_64 x86_64
% 0.15/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.45 % Memory : 8046.5625MB
% 0.15/0.45 % OS : Linux 6.8.0-71-generic
% 0.15/0.45 % CPULimit : 300
% 0.15/0.45 % WCLimit : 300
% 0.15/0.45 % DateTime : Sun Sep 20 20:34:17 UTC 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.48 % Drodi V4.1.1
% 0.15/0.61 % Refutation found
% 0.15/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.67 % Elapsed time: 0.193451 seconds
% 0.15/0.67 % CPU time: 1.008742 seconds
% 0.15/0.67 % Total memory used: 83.807 MB
% 0.15/0.67 % Net memory used: 83.323 MB
%------------------------------------------------------------------------------