%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP685+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 01:28:03 PM UTC 2026
% Result : Theorem 5.97s 6.26s
% Output : Proof 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 9
% Syntax : Number of formulae : 162 ( 157 unt; 0 def)
% Number of atoms : 167 ( 166 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 15 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 351 ( 2 sgn 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [D,C,B,A] : ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] : ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(ld(X3,mult(X3,X1)),X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t6,plain,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
inference(equality_encoding,[status(esa)],[c4]) ).
fof(f2,axiom,
! [B,A] : mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f2_nnf,plain,
! [B,A] : mult(A,ld(A,B)) = ld(A,mult(A,B)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : mult(A,ld(A,B)) = ld(A,mult(A,B)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t17,plain,
ld(X1,mult(X1,X2)) = mult(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t3]) ).
cnf(t1099,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
inference(step,[status(thm)],[t6,t17]) ).
cnf(t1100,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(step,[status(thm)],[t1099,t17]) ).
cnf(t24,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(orient,[status(thm)],[t1100]) ).
cnf(t25,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(mult(X1,ld(X1,X4)),ld(ld(X1,mult(X1,X4)),mult(X2,X3))),
inference(cp,[status(thm)],[t24,t17]) ).
cnf(t1144,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(mult(X1,ld(X1,X4)),ld(mult(X1,ld(X1,X4)),mult(X2,X3))),
inference(step,[status(thm)],[t25,t17]) ).
cnf(t626,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(orient,[status(thm)],[t1144]) ).
fof(f0,axiom,
! [A] : ld(A,mult(A,A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f0_nnf,plain,
! [A] : ld(A,mult(A,A)) = A,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : ld(A,mult(A,A)) = A,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
ld(X1,mult(X1,X1)) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t10,plain,
ld(X1,mult(X1,X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t1098,plain,
mult(X1,ld(X1,X1)) = X1,
inference(step,[status(thm)],[t10,t17]) ).
cnf(t18,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[t1098]) ).
cnf(t37,plain,
mult(X1,ld(X1,X1)) = X1,
inference(orient,[status(thm)],[t18]) ).
cnf(t39,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(cp,[status(thm)],[t17,t37]) ).
fof(f6,axiom,
! [B,A] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f6_nnf,plain,
! [B,A] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
ld(X1,mult(X1,ld(X0,X0))) = rd(mult(rd(X1,X1),X0),X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t5,plain,
rd(mult(rd(X1,X1),X2),X2) = ld(X1,mult(X1,ld(X2,X2))),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t1101,plain,
rd(mult(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(step,[status(thm)],[t5,t17]) ).
cnf(t32,plain,
mult(X1,ld(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t1101]) ).
cnf(t1102,plain,
rd(mult(rd(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t39,t32]) ).
fof(f3,axiom,
! [B,A] : mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f3_nnf,plain,
! [B,A] : mult(rd(A,B),B) = rd(mult(A,B),B),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : mult(rd(A,B),B) = rd(mult(A,B),B),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t4,plain,
rd(mult(X1,X2),X2) = mult(rd(X1,X2),X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t19,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t4]) ).
cnf(t1103,plain,
rd(rd(mult(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t1102,t19]) ).
fof(f1,axiom,
! [A] : rd(mult(A,A),A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f1_nnf,plain,
! [A] : rd(mult(A,A),A) = A,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A] : rd(mult(A,A),A) = A,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
rd(mult(X1,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t9,plain,
rd(mult(X1,X1),X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t1104,plain,
rd(X1,X1) = ld(X1,X1),
inference(step,[status(thm)],[t1103,t9]) ).
cnf(t42,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t1104]) ).
cnf(t630,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(mult(X1,rd(X1,X1)),ld(mult(X1,ld(X1,X1)),mult(X2,X3))),
inference(cp,[status(thm)],[t626,t42]) ).
cnf(t1105,plain,
mult(X1,rd(X1,X1)) = X1,
inference(step,[status(thm)],[t37,t42]) ).
cnf(t45,plain,
mult(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[t1105]) ).
cnf(t47,plain,
mult(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t45]) ).
cnf(t1145,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(mult(X1,ld(X1,X1)),mult(X2,X3))),
inference(step,[status(thm)],[t630,t47]) ).
cnf(t1146,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(mult(X1,rd(X1,X1)),mult(X2,X3))),
inference(step,[status(thm)],[t1145,t42]) ).
cnf(t1147,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(step,[status(thm)],[t1146,t47]) ).
cnf(t681,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(orient,[status(thm)],[t1147]) ).
cnf(t694,plain,
mult(X1,ld(X1,mult(X1,X2))) = mult(mult(X1,rd(X1,X1)),X2),
inference(cp,[status(thm)],[t681,t42]) ).
cnf(t1154,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(mult(X1,rd(X1,X1)),X2),
inference(step,[status(thm)],[t694,t17]) ).
cnf(t1155,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(step,[status(thm)],[t1154,t47]) ).
cnf(t732,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(orient,[status(thm)],[t1155]) ).
cnf(t1106,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(step,[status(thm)],[t32,t42]) ).
cnf(t46,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(rw,[status(thm)],[t1106]) ).
cnf(t90,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t46]) ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f5_nnf,plain,
! [D,C,B,A] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,rd(mult(X2,X0),X0)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t7,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t12,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(orient,[status(thm)],[t7]) ).
cnf(t13,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),rd(mult(X3,X3),X3)),
inference(cp,[status(thm)],[t12,t9]) ).
cnf(t1108,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),X3),
inference(step,[status(thm)],[t13,t9]) ).
cnf(t61,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),X3),
inference(orient,[status(thm)],[t1108]) ).
cnf(t1109,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = rd(mult(mult(X1,X2),X4),X4),
inference(step,[status(thm)],[t12,t61]) ).
cnf(t62,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = rd(mult(mult(X1,X2),X4),X4),
inference(orient,[status(thm)],[t1109]) ).
cnf(t91,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = mult(rd(X1,X1),rd(rd(X1,X1),rd(X1,X1))),
inference(cp,[status(thm)],[t90,t42]) ).
cnf(t1113,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = rd(X1,X1),
inference(step,[status(thm)],[t91,t47]) ).
cnf(t113,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = rd(X1,X1),
inference(orient,[status(thm)],[t1113]) ).
cnf(t115,plain,
rd(mult(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1),X1) = mult(rd(X1,X1),X1),
inference(cp,[status(thm)],[t19,t113]) ).
cnf(t65,plain,
rd(mult(mult(X1,X2),X2),X2) = mult(X1,X2),
inference(cp,[status(thm)],[t61,t9]) ).
cnf(t79,plain,
rd(mult(mult(X1,X2),X2),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t65]) ).
cnf(t1114,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = mult(rd(X1,X1),X1),
inference(step,[status(thm)],[t115,t79]) ).
cnf(t1115,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = rd(mult(X1,X1),X1),
inference(step,[status(thm)],[t1114,t19]) ).
cnf(t1116,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(step,[status(thm)],[t1115,t9]) ).
cnf(t119,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(orient,[status(thm)],[t1116]) ).
cnf(t122,plain,
rd(mult(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X2),X2) = rd(mult(X1,rd(X3,X2)),rd(X3,X2)),
inference(cp,[status(thm)],[t62,t119]) ).
cnf(t1119,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,rd(X3,X2)),rd(X3,X2)),
inference(step,[status(thm)],[t122,t119]) ).
cnf(t132,plain,
rd(mult(X1,rd(X2,X3)),rd(X2,X3)) = rd(mult(X1,X3),X3),
inference(orient,[status(thm)],[t1119]) ).
cnf(t43,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(rd(X1,X1),ld(ld(X1,X1),mult(X2,X3))),
inference(cp,[status(thm)],[t24,t42]) ).
cnf(t1129,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(rd(X1,X1),ld(rd(X1,X1),mult(X2,X3))),
inference(step,[status(thm)],[t43,t42]) ).
cnf(t344,plain,
mult(rd(X1,X1),ld(rd(X1,X1),mult(X2,X3))) = mult(mult(X1,ld(X1,X2)),X3),
inference(orient,[status(thm)],[t1129]) ).
cnf(t136,plain,
rd(mult(rd(X1,rd(X2,X3)),X3),X3) = rd(rd(mult(X1,rd(X2,X3)),rd(X2,X3)),rd(X2,X3)),
inference(cp,[status(thm)],[t132,t19]) ).
cnf(t80,plain,
mult(X1,rd(X2,X3)) = rd(mult(mult(X1,rd(X2,X3)),X3),X3),
inference(cp,[status(thm)],[t79,t62]) ).
cnf(t97,plain,
rd(mult(mult(X1,rd(X2,X3)),X3),X3) = mult(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t80]) ).
cnf(t125,plain,
mult(rd(rd(rd(X1,X2),rd(X1,X2)),rd(rd(X1,X2),rd(X1,X2))),rd(X1,X2)) = rd(mult(rd(X1,X2),X2),X2),
inference(cp,[status(thm)],[t97,t119]) ).
cnf(t1117,plain,
rd(X1,X2) = rd(mult(rd(X1,X2),X2),X2),
inference(step,[status(thm)],[t125,t119]) ).
cnf(t1118,plain,
rd(X1,X2) = rd(rd(mult(X1,X2),X2),X2),
inference(step,[status(thm)],[t1117,t19]) ).
cnf(t126,plain,
rd(rd(mult(X1,X2),X2),X2) = rd(X1,X2),
inference(orient,[status(thm)],[t1118]) ).
cnf(t1122,plain,
rd(mult(rd(X1,rd(X2,X3)),X3),X3) = rd(X1,rd(X2,X3)),
inference(step,[status(thm)],[t136,t126]) ).
cnf(t150,plain,
rd(mult(rd(X1,rd(X2,X3)),X3),X3) = rd(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t1122]) ).
cnf(t152,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(cp,[status(thm)],[t150,t119]) ).
cnf(t163,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t152]) ).
cnf(t164,plain,
rd(X1,X1) = mult(rd(X1,X1),rd(X1,X1)),
inference(cp,[status(thm)],[t47,t163]) ).
cnf(t166,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t164]) ).
cnf(t358,plain,
mult(mult(X1,ld(X1,rd(X2,X2))),rd(X2,X2)) = mult(rd(X1,X1),ld(rd(X1,X1),rd(X2,X2))),
inference(cp,[status(thm)],[t344,t166]) ).
cnf(t1130,plain,
mult(rd(mult(rd(X1,X1),X2),X2),rd(X2,X2)) = mult(rd(X1,X1),ld(rd(X1,X1),rd(X2,X2))),
inference(step,[status(thm)],[t358,t90]) ).
cnf(t144,plain,
rd(mult(mult(X1,rd(X2,X3)),rd(X2,X3)),rd(X2,X3)) = mult(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(cp,[status(thm)],[t19,t132]) ).
cnf(t1124,plain,
rd(mult(mult(X1,rd(X2,X3)),X3),X3) = mult(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(step,[status(thm)],[t144,t62]) ).
cnf(t1125,plain,
mult(X1,rd(X2,X3)) = mult(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(step,[status(thm)],[t1124,t97]) ).
cnf(t185,plain,
mult(rd(mult(X1,X2),X2),rd(X3,X2)) = mult(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t1125]) ).
cnf(t1131,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(X1,X1),ld(rd(X1,X1),rd(X2,X2))),
inference(step,[status(thm)],[t1130,t185]) ).
cnf(t1132,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(rd(X1,X1),rd(X1,X1)),X2),X2),
inference(step,[status(thm)],[t1131,t90]) ).
cnf(t1133,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(X1,X1),X2),X2),
inference(step,[status(thm)],[t1132,t163]) ).
cnf(t380,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t1133]) ).
cnf(t394,plain,
rd(mult(rd(X1,X1),X2),X2) = rd(rd(mult(rd(X1,X1),X2),X2),rd(X2,X2)),
inference(cp,[status(thm)],[t132,t380]) ).
cnf(t145,plain,
rd(X1,rd(X2,X3)) = rd(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(cp,[status(thm)],[t126,t132]) ).
cnf(t202,plain,
rd(rd(mult(X1,X2),X2),rd(X3,X2)) = rd(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t145]) ).
cnf(t1134,plain,
rd(mult(rd(X1,X1),X2),X2) = rd(rd(X1,X1),rd(X2,X2)),
inference(step,[status(thm)],[t394,t202]) ).
cnf(t401,plain,
rd(mult(rd(X1,X1),X2),X2) = rd(rd(X1,X1),rd(X2,X2)),
inference(orient,[status(thm)],[t1134]) ).
cnf(t1135,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(rd(X1,X1),rd(X2,X2)),
inference(step,[status(thm)],[t90,t401]) ).
cnf(t402,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(rd(X1,X1),rd(X2,X2)),
inference(orient,[status(thm)],[t1135]) ).
cnf(t734,plain,
mult(X1,rd(X2,X2)) = mult(X1,rd(rd(X1,X1),rd(X2,X2))),
inference(cp,[status(thm)],[t732,t402]) ).
cnf(t395,plain,
rd(mult(mult(X1,rd(X2,X2)),rd(X3,X3)),rd(X3,X3)) = mult(X1,rd(rd(mult(rd(X2,X2),X3),X3),rd(X3,X3))),
inference(cp,[status(thm)],[t61,t380]) ).
cnf(t1141,plain,
rd(mult(mult(X1,rd(X2,X2)),X3),X3) = mult(X1,rd(rd(mult(rd(X2,X2),X3),X3),rd(X3,X3))),
inference(step,[status(thm)],[t395,t62]) ).
cnf(t1142,plain,
rd(mult(mult(X1,rd(X2,X2)),X3),X3) = mult(X1,rd(rd(X2,X2),rd(X3,X3))),
inference(step,[status(thm)],[t1141,t202]) ).
cnf(t456,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(mult(mult(X1,rd(X2,X2)),X3),X3),
inference(orient,[status(thm)],[t1142]) ).
cnf(t1159,plain,
mult(X1,rd(X2,X2)) = rd(mult(mult(X1,rd(X1,X1)),X2),X2),
inference(step,[status(thm)],[t734,t456]) ).
cnf(t1160,plain,
mult(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(step,[status(thm)],[t1159,t47]) ).
cnf(t764,plain,
mult(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t1160]) ).
cnf(t768,plain,
rd(mult(rd(X1,rd(X2,X2)),X2),X2) = rd(mult(X1,rd(X2,X2)),rd(X2,X2)),
inference(cp,[status(thm)],[t764,t19]) ).
cnf(t1163,plain,
rd(X1,rd(X2,X2)) = rd(mult(X1,rd(X2,X2)),rd(X2,X2)),
inference(step,[status(thm)],[t768,t150]) ).
cnf(t1164,plain,
rd(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(step,[status(thm)],[t1163,t132]) ).
cnf(t795,plain,
rd(mult(X1,X2),X2) = rd(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t1164]) ).
cnf(t140,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,mult(X3,X2)),rd(mult(mult(X3,X2),X2),X2)),
inference(cp,[status(thm)],[t132,t79]) ).
cnf(t1123,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,mult(X3,X2)),mult(X3,X2)),
inference(step,[status(thm)],[t140,t79]) ).
cnf(t168,plain,
rd(mult(X1,mult(X2,X3)),mult(X2,X3)) = rd(mult(X1,X3),X3),
inference(orient,[status(thm)],[t1123]) ).
cnf(t1179,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(mult(X1,X3),X3),
inference(step,[status(thm)],[t168,t795]) ).
cnf(t1180,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1179,t795]) ).
cnf(t819,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(rw,[status(thm)],[t1180]) ).
cnf(t917,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t819]) ).
cnf(t922,plain,
rd(X1,rd(mult(X2,ld(X2,X3)),mult(X2,ld(X2,X3)))) = rd(X1,rd(mult(X2,X3),mult(X2,mult(X2,ld(X2,X3))))),
inference(cp,[status(thm)],[t917,t732]) ).
cnf(t1202,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(mult(X2,X3),mult(X2,mult(X2,ld(X2,X3))))),
inference(step,[status(thm)],[t922,t917]) ).
cnf(t1203,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(mult(X2,X3),mult(X2,X3))),
inference(step,[status(thm)],[t1202,t732]) ).
cnf(t1204,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1203,t917]) ).
cnf(t1057,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t1204]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f7_neg,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)],[f7]) ).
fof(f7_nnf,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(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( 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(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f7_nnf]) ).
cnf(c7,plain,
( 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,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
true != ifeq(rd(mult(sk0,ld(sk1,sk2)),ld(sk1,sk2)),rd(mult(sk0,sk2),sk2),ifeq(rd(mult(sk0,rd(sk1,sk2)),rd(sk1,sk2)),rd(mult(sk0,sk2),sk2),false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(rd(mult(sk0,ld(sk1,sk2)),ld(sk1,sk2)),rd(mult(sk0,sk2),sk2),ifeq(rd(mult(sk0,sk2),sk2),rd(mult(sk0,sk2),sk2),false,true),true),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
true != ifeq(rd(mult(sk0,ld(sk1,sk2)),ld(sk1,sk2)),rd(sk0,rd(sk2,sk2)),ifeq(rd(mult(sk0,sk2),sk2),rd(mult(sk0,sk2),sk2),false,true),true),
inference(rw,[status(thm)],[g0_1,t795]) ).
cnf(g0_3,plain,
true != ifeq(rd(sk0,rd(ld(sk1,sk2),ld(sk1,sk2))),rd(sk0,rd(sk2,sk2)),ifeq(rd(mult(sk0,sk2),sk2),rd(mult(sk0,sk2),sk2),false,true),true),
inference(rw,[status(thm)],[g0_2,t795]) ).
cnf(g0_4,plain,
true != ifeq(rd(sk0,rd(sk2,sk2)),rd(sk0,rd(sk2,sk2)),ifeq(rd(mult(sk0,sk2),sk2),rd(mult(sk0,sk2),sk2),false,true),true),
inference(rw,[status(thm)],[g0_3,t1057]) ).
cnf(g0_5,plain,
true != ifeq(rd(mult(sk0,sk2),sk2),rd(mult(sk0,sk2),sk2),false,true),
inference(rw,[status(thm)],[g0_4,t11]) ).
cnf(g0_6,plain,
true != false,
inference(rw,[status(thm)],[g0_5,t11]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP685+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.39 % Computer : n001.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Wed Sep 23 15:47:57 UTC 2026
% 0.10/5.40 % CPUTime :
% 0.10/5.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.97/6.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.97/6.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------