%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP660+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:27:57 PM UTC 2026
% Result : Theorem 5.00s 1.14s
% Output : Proof 5.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 7
% Syntax : Number of formulae : 196 ( 191 unt; 0 def)
% Number of atoms : 201 ( 200 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 14 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 385 ( 2 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f3_nnf,plain,
! [B,A] : rd(mult(A,B),B) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t4,plain,
rd(mult(X1,X2),X2) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t9,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
fof(f4,axiom,
! [C,B,A] : mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [C,B,A] : mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
mult(mult(mult(X2,X1),X0),X2) = mult(X2,mult(X1,mult(X0,X2))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
mult(mult(mult(X1,X2),X3),X1) = mult(X1,mult(X2,mult(X3,X1))),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t14,plain,
mult(mult(mult(X1,X2),X3),X1) = mult(X1,mult(X2,mult(X3,X1))),
inference(orient,[status(thm)],[t5]) ).
fof(f0,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f0_nnf,plain,
! [B,A] : mult(A,ld(A,B)) = B,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : mult(A,ld(A,B)) = B,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
mult(X1,ld(X1,X2)) = X2,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t7,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t16,plain,
mult(X1,mult(ld(X1,X2),mult(X3,X1))) = mult(mult(X2,X3),X1),
inference(cp,[status(thm)],[t14,t7]) ).
cnf(t25,plain,
mult(X1,mult(ld(X1,X2),mult(X3,X1))) = mult(mult(X2,X3),X1),
inference(orient,[status(thm)],[t16]) ).
fof(f2,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f2_nnf,plain,
! [B,A] : mult(rd(A,B),B) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
mult(rd(X1,X0),X0) = X1,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
mult(rd(X1,X2),X2) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t8,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t29,plain,
mult(mult(X1,rd(X2,X3)),X3) = mult(X3,mult(ld(X3,X1),X2)),
inference(cp,[status(thm)],[t25,t8]) ).
cnf(t35,plain,
mult(mult(X1,rd(X2,X3)),X3) = mult(X3,mult(ld(X3,X1),X2)),
inference(orient,[status(thm)],[t29]) ).
cnf(t40,plain,
mult(X1,rd(X2,X3)) = rd(mult(X3,mult(ld(X3,X1),X2)),X3),
inference(cp,[status(thm)],[t9,t35]) ).
cnf(t85,plain,
rd(mult(X1,mult(ld(X1,X2),X3)),X1) = mult(X2,rd(X3,X1)),
inference(orient,[status(thm)],[t40]) ).
fof(f1,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f1_nnf,plain,
! [B,A] : ld(A,mult(A,B)) = B,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t1,plain,
ld(X1,mult(X1,X2)) = X2,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t12,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t86,plain,
mult(X1,rd(ld(ld(X2,X1),X3),X2)) = rd(mult(X2,X3),X2),
inference(cp,[status(thm)],[t85,t7]) ).
cnf(t177,plain,
mult(X1,rd(ld(ld(X2,X1),X3),X2)) = rd(mult(X2,X3),X2),
inference(orient,[status(thm)],[t86]) ).
cnf(t183,plain,
rd(ld(ld(X1,X2),X3),X1) = ld(X2,rd(mult(X1,X3),X1)),
inference(cp,[status(thm)],[t12,t177]) ).
cnf(t195,plain,
ld(X1,rd(mult(X2,X3),X2)) = rd(ld(ld(X2,X1),X3),X2),
inference(orient,[status(thm)],[t183]) ).
cnf(t202,plain,
rd(ld(ld(X1,X2),ld(X1,X3)),X1) = ld(X2,rd(X3,X1)),
inference(cp,[status(thm)],[t195,t7]) ).
cnf(t632,plain,
rd(ld(ld(X1,X2),ld(X1,X3)),X1) = ld(X2,rd(X3,X1)),
inference(orient,[status(thm)],[t202]) ).
cnf(t656,plain,
ld(ld(X1,X2),ld(X1,X3)) = mult(ld(X2,rd(X3,X1)),X1),
inference(cp,[status(thm)],[t8,t632]) ).
cnf(t708,plain,
ld(ld(X1,X2),ld(X1,X3)) = mult(ld(X2,rd(X3,X1)),X1),
inference(orient,[status(thm)],[t656]) ).
cnf(t10,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t9,t7]) ).
cnf(t23,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t197,plain,
rd(ld(ld(X1,X2),X1),X1) = ld(X2,X1),
inference(cp,[status(thm)],[t195,t9]) ).
cnf(t218,plain,
rd(ld(ld(X1,X2),X1),X1) = ld(X2,X1),
inference(orient,[status(thm)],[t197]) ).
cnf(t226,plain,
ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1),
inference(cp,[status(thm)],[t8,t218]) ).
cnf(t249,plain,
ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1),
inference(orient,[status(thm)],[t226]) ).
cnf(t256,plain,
ld(X1,X2) = rd(X1,mult(ld(X2,X1),X1)),
inference(cp,[status(thm)],[t23,t249]) ).
cnf(t293,plain,
rd(X1,mult(ld(X2,X1),X1)) = ld(X1,X2),
inference(orient,[status(thm)],[t256]) ).
cnf(t13,plain,
X1 = ld(rd(X2,X1),X2),
inference(cp,[status(thm)],[t12,t8]) ).
cnf(t24,plain,
ld(rd(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t298,plain,
ld(X1,rd(X1,X2)) = rd(X1,mult(X2,X1)),
inference(cp,[status(thm)],[t293,t24]) ).
cnf(t302,plain,
ld(X1,rd(X1,X2)) = rd(X1,mult(X2,X1)),
inference(orient,[status(thm)],[t298]) ).
cnf(t17,plain,
mult(rd(X1,X2),mult(X2,mult(X3,rd(X1,X2)))) = mult(mult(X1,X3),rd(X1,X2)),
inference(cp,[status(thm)],[t14,t8]) ).
cnf(t1078,plain,
mult(rd(X1,X2),mult(X2,mult(X3,rd(X1,X2)))) = mult(mult(X1,X3),rd(X1,X2)),
inference(orient,[status(thm)],[t17]) ).
cnf(t221,plain,
ld(mult(X1,X2),X1) = rd(ld(X2,X1),X1),
inference(cp,[status(thm)],[t218,t12]) ).
cnf(t230,plain,
ld(mult(X1,X2),X1) = rd(ld(X2,X1),X1),
inference(orient,[status(thm)],[t221]) ).
cnf(t241,plain,
mult(X1,X2) = rd(X1,rd(ld(X2,X1),X1)),
inference(cp,[status(thm)],[t23,t230]) ).
cnf(t263,plain,
rd(X1,rd(ld(X2,X1),X1)) = mult(X1,X2),
inference(orient,[status(thm)],[t241]) ).
cnf(t268,plain,
mult(X1,rd(X1,X2)) = rd(X1,rd(X2,X1)),
inference(cp,[status(thm)],[t263,t24]) ).
cnf(t272,plain,
mult(X1,rd(X1,X2)) = rd(X1,rd(X2,X1)),
inference(orient,[status(thm)],[t268]) ).
cnf(t303,plain,
rd(mult(X1,X2),mult(X1,mult(X1,X2))) = rd(ld(ld(X1,mult(X1,X2)),X2),X1),
inference(cp,[status(thm)],[t302,t195]) ).
cnf(t9544,plain,
rd(mult(X1,X2),mult(X1,mult(X1,X2))) = rd(ld(X2,X2),X1),
inference(step,[status(thm)],[t303,t12]) ).
cnf(t1006,plain,
rd(mult(X1,X2),mult(X1,mult(X1,X2))) = rd(ld(X2,X2),X1),
inference(orient,[status(thm)],[t9544]) ).
cnf(t30,plain,
mult(ld(X1,X2),mult(X3,X1)) = ld(X1,mult(mult(X2,X3),X1)),
inference(cp,[status(thm)],[t12,t25]) ).
cnf(t45,plain,
ld(X1,mult(mult(X2,X3),X1)) = mult(ld(X1,X2),mult(X3,X1)),
inference(orient,[status(thm)],[t30]) ).
cnf(t49,plain,
mult(ld(X1,X2),mult(ld(X2,X3),X1)) = ld(X1,mult(X3,X1)),
inference(cp,[status(thm)],[t45,t7]) ).
cnf(t93,plain,
mult(ld(X1,X2),mult(ld(X2,X3),X1)) = ld(X1,mult(X3,X1)),
inference(orient,[status(thm)],[t49]) ).
cnf(t1021,plain,
rd(ld(X1,X1),ld(X1,X1)) = rd(mult(ld(X1,X1),X1),ld(X1,mult(X1,X1))),
inference(cp,[status(thm)],[t1006,t93]) ).
cnf(t9545,plain,
rd(ld(X1,X1),ld(X1,X1)) = rd(mult(ld(X1,X1),X1),X1),
inference(step,[status(thm)],[t1021,t12]) ).
cnf(t9546,plain,
rd(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(step,[status(thm)],[t9545,t9]) ).
cnf(t1054,plain,
rd(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(orient,[status(thm)],[t9546]) ).
cnf(t1063,plain,
rd(ld(X1,X1),rd(ld(X1,X1),ld(X1,X1))) = mult(ld(X1,X1),ld(X1,X1)),
inference(cp,[status(thm)],[t272,t1054]) ).
cnf(t9547,plain,
rd(ld(X1,X1),ld(X1,X1)) = mult(ld(X1,X1),ld(X1,X1)),
inference(step,[status(thm)],[t1063,t1054]) ).
cnf(t9548,plain,
ld(X1,X1) = mult(ld(X1,X1),ld(X1,X1)),
inference(step,[status(thm)],[t9547,t1054]) ).
cnf(t1143,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(orient,[status(thm)],[t9548]) ).
cnf(t1169,plain,
mult(X1,rd(ld(X1,X1),X1)) = rd(mult(X1,ld(X1,X1)),X1),
inference(cp,[status(thm)],[t85,t1143]) ).
cnf(t19,plain,
mult(mult(X1,X2),X3) = rd(mult(X1,mult(X2,mult(X3,X1))),X1),
inference(cp,[status(thm)],[t9,t14]) ).
cnf(t56,plain,
rd(mult(X1,mult(X2,mult(X3,X1))),X1) = mult(mult(X1,X2),X3),
inference(orient,[status(thm)],[t19]) ).
cnf(t60,plain,
mult(mult(X1,rd(X2,mult(X3,X1))),X3) = rd(mult(X1,X2),X1),
inference(cp,[status(thm)],[t56,t8]) ).
cnf(t129,plain,
mult(mult(X1,rd(X2,mult(X3,X1))),X3) = rd(mult(X1,X2),X1),
inference(orient,[status(thm)],[t60]) ).
cnf(t142,plain,
mult(X1,rd(X2,mult(X3,X1))) = rd(rd(mult(X1,X2),X1),X3),
inference(cp,[status(thm)],[t9,t129]) ).
cnf(t152,plain,
mult(X1,rd(X2,mult(X3,X1))) = rd(rd(mult(X1,X2),X1),X3),
inference(orient,[status(thm)],[t142]) ).
cnf(t162,plain,
rd(rd(mult(X1,X2),X1),rd(X3,X1)) = mult(X1,rd(X2,X3)),
inference(cp,[status(thm)],[t152,t8]) ).
cnf(t561,plain,
rd(rd(mult(X1,X2),X1),rd(X3,X1)) = mult(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t162]) ).
cnf(t567,plain,
mult(X1,rd(ld(X1,X2),X3)) = rd(rd(X2,X1),rd(X3,X1)),
inference(cp,[status(thm)],[t561,t7]) ).
cnf(t597,plain,
mult(X1,rd(ld(X1,X2),X3)) = rd(rd(X2,X1),rd(X3,X1)),
inference(orient,[status(thm)],[t567]) ).
cnf(t9551,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(mult(X1,ld(X1,X1)),X1),
inference(step,[status(thm)],[t1169,t597]) ).
cnf(t9552,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(step,[status(thm)],[t9551,t7]) ).
cnf(t1230,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t9552]) ).
cnf(t1235,plain,
rd(rd(X1,X1),rd(rd(X1,X1),rd(X1,X1))) = mult(rd(X1,X1),rd(X1,X1)),
inference(cp,[status(thm)],[t272,t1230]) ).
cnf(t9553,plain,
rd(rd(X1,X1),rd(X1,X1)) = mult(rd(X1,X1),rd(X1,X1)),
inference(step,[status(thm)],[t1235,t1230]) ).
cnf(t9554,plain,
rd(X1,X1) = mult(rd(X1,X1),rd(X1,X1)),
inference(step,[status(thm)],[t9553,t1230]) ).
cnf(t1271,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t9554]) ).
cnf(t1287,plain,
mult(mult(X1,rd(X1,X1)),rd(X1,X1)) = mult(rd(X1,X1),mult(X1,rd(X1,X1))),
inference(cp,[status(thm)],[t1078,t1271]) ).
cnf(t65,plain,
mult(mult(X1,X2),rd(X3,X1)) = rd(mult(X1,mult(X2,X3)),X1),
inference(cp,[status(thm)],[t56,t8]) ).
cnf(t68,plain,
mult(mult(X1,X2),rd(X3,X1)) = rd(mult(X1,mult(X2,X3)),X1),
inference(orient,[status(thm)],[t65]) ).
cnf(t9561,plain,
rd(mult(X1,mult(rd(X1,X1),X1)),X1) = mult(rd(X1,X1),mult(X1,rd(X1,X1))),
inference(step,[status(thm)],[t1287,t68]) ).
cnf(t9562,plain,
rd(mult(X1,X1),X1) = mult(rd(X1,X1),mult(X1,rd(X1,X1))),
inference(step,[status(thm)],[t9561,t8]) ).
cnf(t9563,plain,
X1 = mult(rd(X1,X1),mult(X1,rd(X1,X1))),
inference(step,[status(thm)],[t9562,t9]) ).
cnf(t9564,plain,
X1 = mult(rd(X1,X1),rd(X1,rd(X1,X1))),
inference(step,[status(thm)],[t9563,t272]) ).
cnf(t1471,plain,
mult(rd(X1,X1),rd(X1,rd(X1,X1))) = X1,
inference(orient,[status(thm)],[t9564]) ).
cnf(t1479,plain,
rd(X1,rd(X1,X1)) = ld(rd(X1,X1),X1),
inference(cp,[status(thm)],[t12,t1471]) ).
cnf(t9565,plain,
rd(X1,rd(X1,X1)) = X1,
inference(step,[status(thm)],[t1479,t24]) ).
cnf(t1503,plain,
rd(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t9565]) ).
cnf(t1507,plain,
rd(X1,mult(rd(X1,X1),X1)) = ld(X1,X1),
inference(cp,[status(thm)],[t302,t1503]) ).
cnf(t9566,plain,
rd(X1,X1) = ld(X1,X1),
inference(step,[status(thm)],[t1507,t8]) ).
cnf(t1524,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t9566]) ).
cnf(t1534,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(rd(X1,X1),ld(X1,X2)),
inference(cp,[status(thm)],[t708,t1524]) ).
cnf(t2007,plain,
ld(rd(X1,X1),ld(X1,X2)) = mult(ld(X1,rd(X2,X1)),X1),
inference(orient,[status(thm)],[t1534]) ).
cnf(t46,plain,
mult(ld(mult(X1,X2),X1),mult(X2,mult(X1,X2))) = mult(X1,X2),
inference(cp,[status(thm)],[t45,t12]) ).
cnf(t9624,plain,
mult(rd(ld(X2,X1),X1),mult(X2,mult(X1,X2))) = mult(X1,X2),
inference(step,[status(thm)],[t46,t230]) ).
cnf(t3686,plain,
mult(rd(ld(X1,X2),X2),mult(X1,mult(X2,X1))) = mult(X2,X1),
inference(orient,[status(thm)],[t9624]) ).
cnf(t627,plain,
mult(X1,mult(ld(X1,X2),ld(X2,X3))) = mult(rd(rd(X3,X2),rd(X1,X2)),X1),
inference(cp,[status(thm)],[t35,t597]) ).
cnf(t8348,plain,
mult(rd(rd(X1,X2),rd(X3,X2)),X3) = mult(X3,mult(ld(X3,X2),ld(X2,X1))),
inference(orient,[status(thm)],[t627]) ).
cnf(t8432,plain,
mult(rd(X1,X1),mult(ld(rd(X1,X1),rd(X1,X1)),ld(rd(X1,X1),X2))) = mult(rd(rd(X2,rd(X1,X1)),rd(X1,X1)),rd(X1,X1)),
inference(cp,[status(thm)],[t8348,t1230]) ).
cnf(t53,plain,
mult(ld(X1,rd(X2,X3)),mult(X3,X1)) = ld(X1,mult(X2,X1)),
inference(cp,[status(thm)],[t45,t8]) ).
cnf(t109,plain,
mult(ld(X1,rd(X2,X3)),mult(X3,X1)) = ld(X1,mult(X2,X1)),
inference(orient,[status(thm)],[t53]) ).
cnf(t122,plain,
ld(X1,rd(X2,X3)) = rd(ld(X1,mult(X2,X1)),mult(X3,X1)),
inference(cp,[status(thm)],[t9,t109]) ).
cnf(t498,plain,
rd(ld(X1,mult(X2,X1)),mult(X3,X1)) = ld(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t122]) ).
cnf(t511,plain,
ld(X1,rd(rd(X2,X1),X3)) = rd(ld(X1,X2),mult(X3,X1)),
inference(cp,[status(thm)],[t498,t8]) ).
cnf(t536,plain,
ld(X1,rd(rd(X2,X1),X3)) = rd(ld(X1,X2),mult(X3,X1)),
inference(orient,[status(thm)],[t511]) ).
cnf(t1514,plain,
rd(ld(rd(X1,X1),X1),mult(X2,rd(X1,X1))) = ld(rd(X1,X1),rd(X1,X2)),
inference(cp,[status(thm)],[t536,t1503]) ).
cnf(t9588,plain,
rd(X1,mult(X2,rd(X1,X1))) = ld(rd(X1,X1),rd(X1,X2)),
inference(step,[status(thm)],[t1514,t24]) ).
cnf(t1915,plain,
ld(rd(X1,X1),rd(X1,X2)) = rd(X1,mult(X2,rd(X1,X1))),
inference(orient,[status(thm)],[t9588]) ).
cnf(t9641,plain,
mult(rd(X1,X1),mult(rd(X1,mult(X1,rd(X1,X1))),ld(rd(X1,X1),X2))) = mult(rd(rd(X2,rd(X1,X1)),rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t8432,t1915]) ).
cnf(t9642,plain,
mult(rd(X1,X1),mult(rd(X1,rd(X1,rd(X1,X1))),ld(rd(X1,X1),X2))) = mult(rd(rd(X2,rd(X1,X1)),rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t9641,t272]) ).
cnf(t9643,plain,
mult(rd(X1,X1),mult(rd(X1,X1),ld(rd(X1,X1),X2))) = mult(rd(rd(X2,rd(X1,X1)),rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t9642,t1503]) ).
cnf(t9644,plain,
mult(rd(X1,X1),X2) = mult(rd(rd(X2,rd(X1,X1)),rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t9643,t7]) ).
cnf(t9645,plain,
mult(rd(X1,X1),X2) = rd(X2,rd(X1,X1)),
inference(step,[status(thm)],[t9644,t8]) ).
cnf(t8512,plain,
mult(rd(X1,X1),X2) = rd(X2,rd(X1,X1)),
inference(orient,[status(thm)],[t9645]) ).
cnf(t8550,plain,
mult(X1,rd(X2,X2)) = mult(rd(ld(rd(X2,X2),X1),X1),rd(mult(X1,rd(X2,X2)),rd(X2,X2))),
inference(cp,[status(thm)],[t3686,t8512]) ).
cnf(t9655,plain,
mult(X1,rd(X2,X2)) = mult(rd(ld(rd(X2,X2),X1),X1),X1),
inference(step,[status(thm)],[t8550,t9]) ).
cnf(t9656,plain,
mult(X1,rd(X2,X2)) = ld(rd(X2,X2),X1),
inference(step,[status(thm)],[t9655,t8]) ).
cnf(t8613,plain,
ld(rd(X1,X1),X2) = mult(X2,rd(X1,X1)),
inference(orient,[status(thm)],[t9656]) ).
cnf(t9659,plain,
mult(ld(X1,X2),rd(X1,X1)) = mult(ld(X1,rd(X2,X1)),X1),
inference(step,[status(thm)],[t2007,t8613]) ).
cnf(t8684,plain,
mult(ld(X1,X2),rd(X1,X1)) = mult(ld(X1,rd(X2,X1)),X1),
inference(rw,[status(thm)],[t9659]) ).
cnf(t8997,plain,
mult(ld(X1,rd(X2,X1)),X1) = mult(ld(X1,X2),rd(X1,X1)),
inference(orient,[status(thm)],[t8684]) ).
cnf(t9106,plain,
mult(rd(X1,X2),rd(X2,X2)) = rd(mult(X2,mult(ld(X2,X1),rd(X2,X2))),X2),
inference(cp,[status(thm)],[t85,t8997]) ).
cnf(t9663,plain,
mult(rd(X1,X2),rd(X2,X2)) = mult(X1,rd(rd(X2,X2),X2)),
inference(step,[status(thm)],[t9106,t85]) ).
cnf(t1065,plain,
ld(X1,X1) = ld(ld(X1,X1),ld(X1,X1)),
inference(cp,[status(thm)],[t24,t1054]) ).
cnf(t9549,plain,
ld(X1,X1) = mult(ld(X1,rd(X1,X1)),X1),
inference(step,[status(thm)],[t1065,t708]) ).
cnf(t9550,plain,
ld(X1,X1) = mult(rd(X1,mult(X1,X1)),X1),
inference(step,[status(thm)],[t9549,t302]) ).
cnf(t1171,plain,
mult(rd(X1,mult(X1,X1)),X1) = ld(X1,X1),
inference(orient,[status(thm)],[t9550]) ).
cnf(t1176,plain,
rd(X1,mult(X1,X1)) = rd(ld(X1,X1),X1),
inference(cp,[status(thm)],[t9,t1171]) ).
cnf(t1201,plain,
rd(ld(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(orient,[status(thm)],[t1176]) ).
cnf(t9575,plain,
rd(rd(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(step,[status(thm)],[t1201,t1524]) ).
cnf(t1550,plain,
rd(rd(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(rw,[status(thm)],[t9575]) ).
cnf(t1552,plain,
rd(rd(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(orient,[status(thm)],[t1550]) ).
cnf(t9664,plain,
mult(rd(X1,X2),rd(X2,X2)) = mult(X1,rd(X2,mult(X2,X2))),
inference(step,[status(thm)],[t9663,t1552]) ).
cnf(t9293,plain,
mult(rd(X1,X2),rd(X2,X2)) = mult(X1,rd(X2,mult(X2,X2))),
inference(orient,[status(thm)],[t9664]) ).
cnf(t638,plain,
ld(mult(X1,X2),rd(X3,X1)) = rd(ld(X2,ld(X1,X3)),X1),
inference(cp,[status(thm)],[t632,t12]) ).
cnf(t669,plain,
ld(mult(X1,X2),rd(X3,X1)) = rd(ld(X2,ld(X1,X3)),X1),
inference(orient,[status(thm)],[t638]) ).
cnf(t1506,plain,
rd(ld(X1,ld(rd(X2,X2),X2)),rd(X2,X2)) = ld(mult(rd(X2,X2),X1),X2),
inference(cp,[status(thm)],[t669,t1503]) ).
cnf(t9587,plain,
rd(ld(X1,X2),rd(X2,X2)) = ld(mult(rd(X2,X2),X1),X2),
inference(step,[status(thm)],[t1506,t24]) ).
cnf(t1884,plain,
ld(mult(rd(X1,X1),X2),X1) = rd(ld(X2,X1),rd(X1,X1)),
inference(orient,[status(thm)],[t9587]) ).
cnf(t1902,plain,
mult(rd(X1,X1),X2) = rd(X1,rd(ld(X2,X1),rd(X1,X1))),
inference(cp,[status(thm)],[t23,t1884]) ).
cnf(t3071,plain,
rd(X1,rd(ld(X2,X1),rd(X1,X1))) = mult(rd(X1,X1),X2),
inference(orient,[status(thm)],[t1902]) ).
cnf(t3095,plain,
mult(rd(X1,X1),rd(X1,X2)) = rd(X1,rd(X2,rd(X1,X1))),
inference(cp,[status(thm)],[t3071,t24]) ).
cnf(t3127,plain,
mult(rd(X1,X1),rd(X1,X2)) = rd(X1,rd(X2,rd(X1,X1))),
inference(orient,[status(thm)],[t3095]) ).
cnf(t9648,plain,
rd(rd(X1,X2),rd(X1,X1)) = rd(X1,rd(X2,rd(X1,X1))),
inference(step,[status(thm)],[t3127,t8512]) ).
cnf(t8606,plain,
rd(rd(X1,X2),rd(X1,X1)) = rd(X1,rd(X2,rd(X1,X1))),
inference(rw,[status(thm)],[t9648]) ).
cnf(t8824,plain,
rd(rd(X1,X2),rd(X1,X1)) = rd(X1,rd(X2,rd(X1,X1))),
inference(orient,[status(thm)],[t8606]) ).
cnf(t9341,plain,
mult(X1,rd(rd(X2,X2),mult(rd(X2,X2),rd(X2,X2)))) = mult(rd(X1,rd(X2,X2)),rd(X2,rd(X2,rd(X2,X2)))),
inference(cp,[status(thm)],[t9293,t8824]) ).
cnf(t8639,plain,
rd(X1,X1) = rd(X2,mult(X2,rd(X1,X1))),
inference(cp,[status(thm)],[t23,t8613]) ).
cnf(t8746,plain,
rd(X1,mult(X1,rd(X2,X2))) = rd(X2,X2),
inference(orient,[status(thm)],[t8639]) ).
cnf(t9665,plain,
mult(X1,rd(X2,X2)) = mult(rd(X1,rd(X2,X2)),rd(X2,rd(X2,rd(X2,X2)))),
inference(step,[status(thm)],[t9341,t8746]) ).
cnf(t9666,plain,
mult(X1,rd(X2,X2)) = mult(rd(X1,rd(X2,X2)),rd(X2,X2)),
inference(step,[status(thm)],[t9665,t1503]) ).
cnf(t9667,plain,
mult(X1,rd(X2,X2)) = X1,
inference(step,[status(thm)],[t9666,t8]) ).
cnf(t9405,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t9667]) ).
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]) ).
cnf(t9670,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(X1,X2),
inference(step,[status(thm)],[t8997,t9405]) ).
cnf(t9408,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(X1,X2),
inference(orient,[status(thm)],[t9670]) ).
cnf(t9421,plain,
ld(rd(X1,X1),rd(X2,rd(X1,X1))) = ld(rd(X1,X1),X2),
inference(cp,[status(thm)],[t9405,t9408]) ).
cnf(t9668,plain,
ld(rd(X1,X1),X2) = X2,
inference(step,[status(thm)],[t8613,t9405]) ).
cnf(t9406,plain,
ld(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t9668]) ).
cnf(t9675,plain,
rd(X2,rd(X1,X1)) = ld(rd(X1,X1),X2),
inference(step,[status(thm)],[t9421,t9406]) ).
cnf(t9676,plain,
rd(X2,rd(X1,X1)) = X2,
inference(step,[status(thm)],[t9675,t9406]) ).
cnf(t9487,plain,
rd(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t9676]) ).
fof(f5,conjecture,
! [X0,X1] :
( mult(rd(X1,X1),X0) = X0
& mult(X0,rd(X1,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f5_neg,negated_conjecture,
~ ! [X0,X1] :
( mult(rd(X1,X1),X0) = X0
& mult(X0,rd(X1,X1)) = X0 ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [X0,X1] :
( mult(rd(X1,X1),X0) != X0
| mult(X0,rd(X1,X1)) != X0 ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( mult(rd(sk1,sk1),sk0) != sk0
| mult(sk0,rd(sk1,sk1)) != sk0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f5_nnf]) ).
cnf(c5,plain,
( mult(rd(sk1,sk1),sk0) != sk0
| mult(sk0,rd(sk1,sk1)) != sk0 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != ifeq(mult(sk0,rd(sk1,sk1)),sk0,ifeq(mult(rd(sk1,sk1),sk0),sk0,false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(mult(sk0,rd(sk1,sk1)),sk0,ifeq(rd(sk0,rd(sk1,sk1)),sk0,false,true),true),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
true != ifeq(sk0,sk0,ifeq(rd(sk0,rd(sk1,sk1)),sk0,false,true),true),
inference(rw,[status(thm)],[g0_1,t9405]) ).
cnf(g0_3,plain,
true != ifeq(rd(sk0,rd(sk1,sk1)),sk0,false,true),
inference(rw,[status(thm)],[g0_2,t11]) ).
cnf(g0_4,plain,
true != ifeq(sk0,sk0,false,true),
inference(rw,[status(thm)],[g0_3,t9487]) ).
cnf(g0_5,plain,
true != false,
inference(rw,[status(thm)],[g0_4,t11]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP660+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Wed Sep 23 15:32:20 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.00/1.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.00/1.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------