%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP654+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 01:27:51 PM UTC 2026
% Result : Theorem 27.20s 3.83s
% Output : Proof 27.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 137
% Number of leaves : 7
% Syntax : Number of formulae : 335 ( 330 unt; 0 def)
% Number of atoms : 340 ( 339 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 15 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 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 : 777 ( 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(t12,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
fof(f4,axiom,
! [C,B,A] : mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [C,B,A] : mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
mult(X2,mult(X1,mult(X2,X0))) = mult(mult(mult(X2,X1),X2),X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
mult(mult(mult(X1,X2),X1),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t14,plain,
mult(mult(mult(X1,X2),X1),X3) = mult(X1,mult(X2,mult(X1,X3))),
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(X1,X3))) = mult(mult(X2,X1),X3),
inference(cp,[status(thm)],[t14,t7]) ).
cnf(t25,plain,
mult(X1,mult(ld(X1,X2),mult(X1,X3))) = mult(mult(X2,X1),X3),
inference(orient,[status(thm)],[t16]) ).
cnf(t28,plain,
mult(mult(X1,X2),ld(X2,X3)) = mult(X2,mult(ld(X2,X1),X3)),
inference(cp,[status(thm)],[t25,t7]) ).
cnf(t35,plain,
mult(mult(X1,X2),ld(X2,X3)) = mult(X2,mult(ld(X2,X1),X3)),
inference(orient,[status(thm)],[t28]) ).
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(t39,plain,
mult(X1,mult(ld(X1,rd(X2,X1)),X3)) = mult(X2,ld(X1,X3)),
inference(cp,[status(thm)],[t35,t8]) ).
cnf(t69,plain,
mult(X1,mult(ld(X1,rd(X2,X1)),X3)) = mult(X2,ld(X1,X3)),
inference(orient,[status(thm)],[t39]) ).
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(t9,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t77,plain,
mult(ld(X1,rd(X2,X1)),X3) = ld(X1,mult(X2,ld(X1,X3))),
inference(cp,[status(thm)],[t9,t69]) ).
cnf(t85,plain,
ld(X1,mult(X2,ld(X1,X3))) = mult(ld(X1,rd(X2,X1)),X3),
inference(orient,[status(thm)],[t77]) ).
cnf(t86,plain,
mult(ld(X1,rd(X1,X1)),X2) = ld(X1,X2),
inference(cp,[status(thm)],[t85,t9]) ).
cnf(t97,plain,
mult(ld(X1,rd(X1,X1)),X2) = ld(X1,X2),
inference(orient,[status(thm)],[t86]) ).
cnf(t102,plain,
ld(X1,rd(X1,X1)) = rd(ld(X1,X2),X2),
inference(cp,[status(thm)],[t12,t97]) ).
cnf(t130,plain,
ld(X1,rd(X1,X1)) = rd(ld(X1,X2),X2),
inference(orient,[status(thm)],[t102]) ).
cnf(t131,plain,
rd(X1,X1) = mult(X1,rd(ld(X1,X2),X2)),
inference(cp,[status(thm)],[t7,t130]) ).
cnf(t147,plain,
mult(X1,rd(ld(X1,X2),X2)) = rd(X1,X1),
inference(orient,[status(thm)],[t131]) ).
cnf(t150,plain,
rd(X1,X1) = mult(X1,rd(X2,mult(X1,X2))),
inference(cp,[status(thm)],[t147,t9]) ).
cnf(t220,plain,
mult(X1,rd(X2,mult(X1,X2))) = rd(X1,X1),
inference(orient,[status(thm)],[t150]) ).
cnf(t231,plain,
X1 = rd(rd(X1,X1),rd(X2,mult(X1,X2))),
inference(cp,[status(thm)],[t12,t220]) ).
cnf(t341,plain,
rd(rd(X1,X1),rd(X2,mult(X1,X2))) = X1,
inference(orient,[status(thm)],[t231]) ).
cnf(t352,plain,
mult(rd(X1,X1),ld(rd(X2,mult(X1,X2)),X3)) = mult(rd(X2,mult(X1,X2)),mult(ld(rd(X2,mult(X1,X2)),X1),X3)),
inference(cp,[status(thm)],[t69,t341]) ).
cnf(t143,plain,
ld(X1,X2) = mult(ld(X1,rd(X1,X1)),X2),
inference(cp,[status(thm)],[t8,t130]) ).
cnf(t70627,plain,
ld(X1,X2) = mult(rd(ld(X1,true),true),X2),
inference(step,[status(thm)],[t143,t130]) ).
cnf(t163,plain,
mult(rd(ld(X1,true),true),X2) = ld(X1,X2),
inference(orient,[status(thm)],[t70627]) ).
cnf(t10,plain,
X1 = ld(rd(X2,X1),X2),
inference(cp,[status(thm)],[t9,t8]) ).
cnf(t23,plain,
ld(rd(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t168,plain,
ld(rd(true,X1),X2) = mult(rd(X1,true),X2),
inference(cp,[status(thm)],[t163,t23]) ).
cnf(t179,plain,
ld(rd(true,X1),X2) = mult(rd(X1,true),X2),
inference(orient,[status(thm)],[t168]) ).
cnf(t98,plain,
ld(X1,ld(ld(X1,rd(X1,X1)),X2)) = X2,
inference(cp,[status(thm)],[t97,t7]) ).
cnf(t111,plain,
ld(X1,ld(ld(X1,rd(X1,X1)),X2)) = X2,
inference(orient,[status(thm)],[t98]) ).
cnf(t114,plain,
ld(ld(X1,rd(X1,X1)),X2) = mult(X1,X2),
inference(cp,[status(thm)],[t7,t111]) ).
cnf(t120,plain,
ld(ld(X1,rd(X1,X1)),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t114]) ).
cnf(t145,plain,
ld(ld(X1,rd(X1,X1)),X2) = mult(X1,X2),
inference(rw,[status(thm)],[t120]) ).
cnf(t70628,plain,
ld(rd(ld(X1,true),true),X2) = mult(X1,X2),
inference(step,[status(thm)],[t145,t130]) ).
cnf(t192,plain,
ld(rd(ld(X1,true),true),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t70628]) ).
cnf(t196,plain,
mult(rd(true,X1),X2) = ld(rd(X1,true),X2),
inference(cp,[status(thm)],[t192,t23]) ).
cnf(t205,plain,
ld(rd(X1,true),X2) = mult(rd(true,X1),X2),
inference(orient,[status(thm)],[t196]) ).
cnf(t210,plain,
mult(rd(true,mult(X1,true)),X2) = ld(X1,X2),
inference(cp,[status(thm)],[t205,t12]) ).
cnf(t250,plain,
mult(rd(true,mult(X1,true)),X2) = ld(X1,X2),
inference(orient,[status(thm)],[t210]) ).
cnf(t257,plain,
rd(true,mult(X1,true)) = rd(ld(X1,X2),X2),
inference(cp,[status(thm)],[t12,t250]) ).
cnf(t266,plain,
rd(ld(X1,X2),X2) = rd(true,mult(X1,true)),
inference(orient,[status(thm)],[t257]) ).
cnf(t270,plain,
rd(true,mult(rd(X1,X2),true)) = rd(X2,X1),
inference(cp,[status(thm)],[t266,t23]) ).
cnf(t289,plain,
rd(true,mult(rd(X1,X2),true)) = rd(X2,X1),
inference(orient,[status(thm)],[t270]) ).
cnf(t292,plain,
mult(rd(mult(rd(X1,X2),true),true),X3) = ld(rd(X2,X1),X3),
inference(cp,[status(thm)],[t179,t289]) ).
cnf(t70630,plain,
mult(rd(X1,X2),X3) = ld(rd(X2,X1),X3),
inference(step,[status(thm)],[t292,t12]) ).
cnf(t299,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(orient,[status(thm)],[t70630]) ).
cnf(t70632,plain,
mult(rd(X1,X1),mult(rd(mult(X1,X2),X2),X3)) = mult(rd(X2,mult(X1,X2)),mult(ld(rd(X2,mult(X1,X2)),X1),X3)),
inference(step,[status(thm)],[t352,t299]) ).
cnf(t70633,plain,
mult(rd(X1,X1),mult(X1,X3)) = mult(rd(X2,mult(X1,X2)),mult(ld(rd(X2,mult(X1,X2)),X1),X3)),
inference(step,[status(thm)],[t70632,t12]) ).
cnf(t304,plain,
mult(rd(X1,mult(X2,X1)),X3) = ld(X2,X3),
inference(cp,[status(thm)],[t299,t12]) ).
cnf(t322,plain,
mult(rd(X1,mult(X2,X1)),X3) = ld(X2,X3),
inference(orient,[status(thm)],[t304]) ).
cnf(t70634,plain,
mult(rd(X1,X1),mult(X1,X3)) = ld(X1,mult(ld(rd(X2,mult(X1,X2)),X1),X3)),
inference(step,[status(thm)],[t70633,t322]) ).
cnf(t70635,plain,
mult(rd(X1,X1),mult(X1,X3)) = ld(X1,mult(mult(rd(mult(X1,X2),X2),X1),X3)),
inference(step,[status(thm)],[t70634,t299]) ).
cnf(t32,plain,
mult(ld(X1,X2),mult(X1,X3)) = ld(X1,mult(mult(X2,X1),X3)),
inference(cp,[status(thm)],[t9,t25]) ).
cnf(t47,plain,
ld(X1,mult(mult(X2,X1),X3)) = mult(ld(X1,X2),mult(X1,X3)),
inference(orient,[status(thm)],[t32]) ).
cnf(t70636,plain,
mult(rd(X1,X1),mult(X1,X3)) = mult(ld(X1,rd(mult(X1,X2),X2)),mult(X1,X3)),
inference(step,[status(thm)],[t70635,t47]) ).
cnf(t70637,plain,
mult(rd(X1,X1),mult(X1,X3)) = mult(ld(X1,X1),mult(X1,X3)),
inference(step,[status(thm)],[t70636,t12]) ).
cnf(t390,plain,
mult(ld(X1,X1),mult(X1,X2)) = mult(rd(X1,X1),mult(X1,X2)),
inference(orient,[status(thm)],[t70637]) ).
cnf(t404,plain,
ld(X1,X1) = rd(mult(rd(X1,X1),mult(X1,X2)),mult(X1,X2)),
inference(cp,[status(thm)],[t12,t390]) ).
cnf(t70638,plain,
ld(X1,X1) = rd(X1,X1),
inference(step,[status(thm)],[t404,t12]) ).
cnf(t416,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t70638]) ).
cnf(t43,plain,
ld(X1,X2) = ld(mult(X3,X1),mult(X1,mult(ld(X1,X3),X2))),
inference(cp,[status(thm)],[t9,t35]) ).
cnf(t4547,plain,
ld(mult(X1,X2),mult(X2,mult(ld(X2,X1),X3))) = ld(X2,X3),
inference(orient,[status(thm)],[t43]) ).
cnf(t4600,plain,
ld(X1,ld(ld(X1,X2),X3)) = ld(mult(X2,X1),mult(X1,X3)),
inference(cp,[status(thm)],[t4547,t7]) ).
cnf(t4639,plain,
ld(mult(X1,X2),mult(X2,X3)) = ld(X2,ld(ld(X2,X1),X3)),
inference(orient,[status(thm)],[t4600]) ).
cnf(t4712,plain,
ld(rd(X1,X2),ld(ld(rd(X1,X2),X3),X2)) = ld(mult(X3,rd(X1,X2)),X1),
inference(cp,[status(thm)],[t4639,t8]) ).
cnf(t70981,plain,
mult(rd(X2,X1),ld(ld(rd(X1,X2),X3),X2)) = ld(mult(X3,rd(X1,X2)),X1),
inference(step,[status(thm)],[t4712,t299]) ).
cnf(t70982,plain,
mult(rd(X2,X1),ld(mult(rd(X2,X1),X3),X2)) = ld(mult(X3,rd(X1,X2)),X1),
inference(step,[status(thm)],[t70981,t299]) ).
cnf(t47698,plain,
mult(rd(X1,X2),ld(mult(rd(X1,X2),X3),X1)) = ld(mult(X3,rd(X2,X1)),X2),
inference(orient,[status(thm)],[t70982]) ).
cnf(t54,plain,
mult(ld(X1,rd(X2,X1)),mult(X1,X3)) = ld(X1,mult(X2,X3)),
inference(cp,[status(thm)],[t47,t8]) ).
cnf(t561,plain,
mult(ld(X1,rd(X2,X1)),mult(X1,X3)) = ld(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t54]) ).
cnf(t583,plain,
ld(X1,rd(X2,X1)) = rd(ld(X1,mult(X2,X3)),mult(X1,X3)),
inference(cp,[status(thm)],[t12,t561]) ).
cnf(t1422,plain,
rd(ld(X1,mult(X2,X3)),mult(X1,X3)) = ld(X1,rd(X2,X1)),
inference(orient,[status(thm)],[t583]) ).
cnf(t418,plain,
X1 = mult(X1,rd(X1,X1)),
inference(cp,[status(thm)],[t7,t416]) ).
cnf(t425,plain,
mult(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t418]) ).
cnf(t1433,plain,
ld(X1,rd(X2,X1)) = rd(ld(X1,X2),mult(X1,rd(X2,X2))),
inference(cp,[status(thm)],[t1422,t425]) ).
cnf(t2632,plain,
rd(ld(X1,X2),mult(X1,rd(X2,X2))) = ld(X1,rd(X2,X1)),
inference(orient,[status(thm)],[t1433]) ).
cnf(t2639,plain,
ld(X1,rd(mult(X1,X2),X1)) = rd(X2,mult(X1,rd(mult(X1,X2),mult(X1,X2)))),
inference(cp,[status(thm)],[t2632,t9]) ).
cnf(t15,plain,
mult(X1,mult(X2,mult(X1,ld(mult(mult(X1,X2),X1),X3)))) = X3,
inference(cp,[status(thm)],[t14,t7]) ).
cnf(t635,plain,
mult(X1,mult(X2,mult(X1,ld(mult(mult(X1,X2),X1),X3)))) = X3,
inference(orient,[status(thm)],[t15]) ).
cnf(t18,plain,
mult(mult(X1,X2),X1) = rd(mult(X1,mult(X2,mult(X1,X3))),X3),
inference(cp,[status(thm)],[t12,t14]) ).
cnf(t58,plain,
rd(mult(X1,mult(X2,mult(X1,X3))),X3) = mult(mult(X1,X2),X1),
inference(orient,[status(thm)],[t18]) ).
cnf(t338,plain,
mult(mult(rd(X1,mult(X2,X1)),X3),rd(X1,mult(X2,X1))) = rd(ld(X2,mult(X3,mult(rd(X1,mult(X2,X1)),Y3))),Y3),
inference(cp,[status(thm)],[t58,t322]) ).
cnf(t70650,plain,
mult(ld(X2,X3),rd(X1,mult(X2,X1))) = rd(ld(X2,mult(X3,mult(rd(X1,mult(X2,X1)),Y3))),Y3),
inference(step,[status(thm)],[t338,t322]) ).
cnf(t70651,plain,
mult(ld(X2,X3),rd(X1,mult(X2,X1))) = rd(ld(X2,mult(X3,ld(X2,Y3))),Y3),
inference(step,[status(thm)],[t70650,t322]) ).
cnf(t70652,plain,
mult(ld(X2,X3),rd(X1,mult(X2,X1))) = rd(mult(ld(X2,rd(X3,X2)),Y3),Y3),
inference(step,[status(thm)],[t70651,t85]) ).
cnf(t70653,plain,
mult(ld(X2,X3),rd(X1,mult(X2,X1))) = ld(X2,rd(X3,X2)),
inference(step,[status(thm)],[t70652,t12]) ).
cnf(t818,plain,
mult(ld(X1,X2),rd(X3,mult(X1,X3))) = ld(X1,rd(X2,X1)),
inference(orient,[status(thm)],[t70653]) ).
cnf(t854,plain,
mult(X1,ld(X2,rd(X3,mult(X2,X3)))) = mult(X2,ld(X2,rd(rd(X1,X2),X2))),
inference(cp,[status(thm)],[t69,t818]) ).
cnf(t422,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(X1,mult(X2,rd(X1,X1))),
inference(cp,[status(thm)],[t85,t416]) ).
cnf(t495,plain,
ld(X1,mult(X2,rd(X1,X1))) = mult(ld(X1,rd(X2,X1)),X1),
inference(orient,[status(thm)],[t422]) ).
cnf(t228,plain,
rd(rd(X1,X2),rd(X1,X2)) = mult(rd(X1,X2),rd(X2,X1)),
inference(cp,[status(thm)],[t220,t8]) ).
cnf(t370,plain,
mult(rd(X1,X2),rd(X2,X1)) = rd(rd(X1,X2),rd(X1,X2)),
inference(orient,[status(thm)],[t228]) ).
cnf(t498,plain,
mult(ld(X1,rd(rd(X1,X1),X1)),X1) = ld(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(cp,[status(thm)],[t495,t370]) ).
cnf(t419,plain,
rd(true,mult(X1,true)) = rd(rd(X1,X1),X1),
inference(cp,[status(thm)],[t266,t416]) ).
cnf(t449,plain,
rd(rd(X1,X1),X1) = rd(true,mult(X1,true)),
inference(orient,[status(thm)],[t419]) ).
cnf(t70656,plain,
mult(ld(X1,rd(true,mult(X1,true))),X1) = ld(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t498,t449]) ).
cnf(t420,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(mult(X2,X1),rd(X1,X1)),
inference(cp,[status(thm)],[t35,t416]) ).
cnf(t452,plain,
mult(mult(X1,X2),rd(X2,X2)) = mult(X2,mult(ld(X2,X1),X2)),
inference(orient,[status(thm)],[t420]) ).
cnf(t454,plain,
mult(rd(X1,X1),mult(ld(rd(X1,X1),X1),rd(X1,X1))) = mult(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(cp,[status(thm)],[t452,t425]) ).
cnf(t70641,plain,
mult(rd(X1,X1),mult(mult(rd(X1,X1),X1),rd(X1,X1))) = mult(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t454,t299]) ).
cnf(t70642,plain,
mult(rd(X1,X1),mult(X1,rd(X1,X1))) = mult(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t70641,t8]) ).
cnf(t70643,plain,
mult(rd(X1,X1),X1) = mult(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t70642,t425]) ).
cnf(t70644,plain,
X1 = mult(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t70643,t8]) ).
cnf(t475,plain,
mult(X1,rd(rd(X1,X1),rd(X1,X1))) = X1,
inference(orient,[status(thm)],[t70644]) ).
cnf(t481,plain,
rd(rd(X1,X1),rd(X1,X1)) = ld(X1,X1),
inference(cp,[status(thm)],[t9,t475]) ).
cnf(t70645,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(step,[status(thm)],[t481,t416]) ).
cnf(t493,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t70645]) ).
cnf(t70657,plain,
mult(ld(X1,rd(true,mult(X1,true))),X1) = ld(X1,rd(X1,X1)),
inference(step,[status(thm)],[t70656,t493]) ).
cnf(t70629,plain,
ld(X1,rd(X1,X1)) = rd(true,mult(X1,true)),
inference(step,[status(thm)],[t130,t266]) ).
cnf(t273,plain,
ld(X1,rd(X1,X1)) = rd(true,mult(X1,true)),
inference(rw,[status(thm)],[t70629]) ).
cnf(t274,plain,
ld(X1,rd(X1,X1)) = rd(true,mult(X1,true)),
inference(orient,[status(thm)],[t273]) ).
cnf(t70658,plain,
mult(ld(X1,rd(true,mult(X1,true))),X1) = rd(true,mult(X1,true)),
inference(step,[status(thm)],[t70657,t274]) ).
cnf(t1087,plain,
mult(ld(X1,rd(true,mult(X1,true))),X1) = rd(true,mult(X1,true)),
inference(orient,[status(thm)],[t70658]) ).
cnf(t1096,plain,
rd(true,mult(rd(X1,mult(X2,X1)),true)) = mult(ld(rd(X1,mult(X2,X1)),rd(true,ld(X2,true))),rd(X1,mult(X2,X1))),
inference(cp,[status(thm)],[t1087,t322]) ).
cnf(t70659,plain,
rd(mult(X2,X1),X1) = mult(ld(rd(X1,mult(X2,X1)),rd(true,ld(X2,true))),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t1096,t289]) ).
cnf(t70660,plain,
X2 = mult(ld(rd(X1,mult(X2,X1)),rd(true,ld(X2,true))),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t70659,t12]) ).
cnf(t70661,plain,
X2 = mult(mult(rd(mult(X2,X1),X1),rd(true,ld(X2,true))),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t70660,t299]) ).
cnf(t70662,plain,
X2 = mult(mult(X2,rd(true,ld(X2,true))),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t70661,t12]) ).
cnf(t13,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t12,t7]) ).
cnf(t24,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t70663,plain,
X2 = mult(mult(X2,X2),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t70662,t24]) ).
cnf(t1121,plain,
mult(mult(X1,X1),rd(X2,mult(X1,X2))) = X1,
inference(orient,[status(thm)],[t70663]) ).
cnf(t1150,plain,
mult(X1,X1) = rd(X1,rd(X2,mult(X1,X2))),
inference(cp,[status(thm)],[t12,t1121]) ).
cnf(t1167,plain,
rd(X1,rd(X2,mult(X1,X2))) = mult(X1,X1),
inference(orient,[status(thm)],[t1150]) ).
cnf(t1189,plain,
mult(rd(X1,mult(X2,X1)),rd(X1,mult(X2,X1))) = rd(rd(X1,mult(X2,X1)),rd(X3,ld(X2,X3))),
inference(cp,[status(thm)],[t1167,t322]) ).
cnf(t70664,plain,
ld(X2,rd(X1,mult(X2,X1))) = rd(rd(X1,mult(X2,X1)),rd(X3,ld(X2,X3))),
inference(step,[status(thm)],[t1189,t322]) ).
cnf(t70665,plain,
ld(X2,rd(X1,mult(X2,X1))) = rd(rd(X1,mult(X2,X1)),X2),
inference(step,[status(thm)],[t70664,t24]) ).
cnf(t1264,plain,
ld(X1,rd(X2,mult(X1,X2))) = rd(rd(X2,mult(X1,X2)),X1),
inference(orient,[status(thm)],[t70665]) ).
cnf(t1151,plain,
rd(X1,mult(X2,X1)) = ld(mult(X2,X2),X2),
inference(cp,[status(thm)],[t9,t1121]) ).
cnf(t1293,plain,
rd(X1,mult(X2,X1)) = ld(mult(X2,X2),X2),
inference(orient,[status(thm)],[t1151]) ).
cnf(t1331,plain,
rd(true,mult(mult(X1,X1),true)) = rd(rd(X2,mult(X1,X2)),X1),
inference(cp,[status(thm)],[t266,t1293]) ).
cnf(t1338,plain,
rd(rd(X1,mult(X2,X1)),X2) = rd(true,mult(mult(X2,X2),true)),
inference(orient,[status(thm)],[t1331]) ).
cnf(t70666,plain,
ld(X1,rd(X2,mult(X1,X2))) = rd(true,mult(mult(X1,X1),true)),
inference(step,[status(thm)],[t1264,t1338]) ).
cnf(t1339,plain,
ld(X1,rd(X2,mult(X1,X2))) = rd(true,mult(mult(X1,X1),true)),
inference(orient,[status(thm)],[t70666]) ).
cnf(t70679,plain,
mult(X1,rd(true,mult(mult(X2,X2),true))) = mult(X2,ld(X2,rd(rd(X1,X2),X2))),
inference(step,[status(thm)],[t854,t1339]) ).
cnf(t70680,plain,
mult(X1,rd(true,mult(mult(X2,X2),true))) = rd(rd(X1,X2),X2),
inference(step,[status(thm)],[t70679,t7]) ).
cnf(t2063,plain,
mult(X1,rd(true,mult(mult(X2,X2),true))) = rd(rd(X1,X2),X2),
inference(orient,[status(thm)],[t70680]) ).
cnf(t2092,plain,
rd(true,mult(mult(X1,X1),true)) = ld(X2,rd(rd(X2,X1),X1)),
inference(cp,[status(thm)],[t9,t2063]) ).
cnf(t2135,plain,
ld(X1,rd(rd(X1,X2),X2)) = rd(true,mult(mult(X2,X2),true)),
inference(orient,[status(thm)],[t2092]) ).
cnf(t2147,plain,
rd(true,mult(mult(X1,X1),true)) = ld(mult(X2,X1),rd(X2,X1)),
inference(cp,[status(thm)],[t2135,t12]) ).
cnf(t2192,plain,
ld(mult(X1,X2),rd(X1,X2)) = rd(true,mult(mult(X2,X2),true)),
inference(orient,[status(thm)],[t2147]) ).
cnf(t2246,plain,
rd(mult(X1,X2),X1) = mult(X1,mult(X2,mult(X1,rd(true,mult(mult(X1,X1),true))))),
inference(cp,[status(thm)],[t635,t2192]) ).
cnf(t70698,plain,
rd(mult(X1,X2),X1) = mult(X1,mult(X2,rd(rd(X1,X1),X1))),
inference(step,[status(thm)],[t2246,t2063]) ).
cnf(t70699,plain,
rd(mult(X1,X2),X1) = mult(X1,mult(X2,rd(true,mult(X1,true)))),
inference(step,[status(thm)],[t70698,t449]) ).
cnf(t3228,plain,
mult(X1,mult(X2,rd(true,mult(X1,true)))) = rd(mult(X1,X2),X1),
inference(orient,[status(thm)],[t70699]) ).
cnf(t3257,plain,
mult(X1,rd(true,mult(X2,true))) = ld(X2,rd(mult(X2,X1),X2)),
inference(cp,[status(thm)],[t9,t3228]) ).
cnf(t3299,plain,
ld(X1,rd(mult(X1,X2),X1)) = mult(X2,rd(true,mult(X1,true))),
inference(orient,[status(thm)],[t3257]) ).
cnf(t70930,plain,
mult(X2,rd(true,mult(X1,true))) = rd(X2,mult(X1,rd(mult(X1,X2),mult(X1,X2)))),
inference(step,[status(thm)],[t2639,t3299]) ).
cnf(t62,plain,
mult(mult(X1,rd(X2,mult(X1,X3))),X1) = rd(mult(X1,X2),X3),
inference(cp,[status(thm)],[t58,t8]) ).
cnf(t595,plain,
mult(mult(X1,rd(X2,mult(X1,X3))),X1) = rd(mult(X1,X2),X3),
inference(orient,[status(thm)],[t62]) ).
cnf(t603,plain,
rd(mult(X1,X2),ld(X1,X3)) = mult(mult(X1,rd(X2,X3)),X1),
inference(cp,[status(thm)],[t595,t7]) ).
cnf(t730,plain,
mult(mult(X1,rd(X2,X3)),X1) = rd(mult(X1,X2),ld(X1,X3)),
inference(orient,[status(thm)],[t603]) ).
cnf(t752,plain,
mult(X1,rd(X2,X3)) = rd(rd(mult(X1,X2),ld(X1,X3)),X1),
inference(cp,[status(thm)],[t12,t730]) ).
cnf(t1674,plain,
rd(rd(mult(X1,X2),ld(X1,X3)),X1) = mult(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t752]) ).
cnf(t1706,plain,
mult(X1,rd(X2,mult(X1,X3))) = rd(rd(mult(X1,X2),X3),X1),
inference(cp,[status(thm)],[t1674,t9]) ).
cnf(t1828,plain,
mult(X1,rd(X2,mult(X1,X3))) = rd(rd(mult(X1,X2),X3),X1),
inference(orient,[status(thm)],[t1706]) ).
cnf(t70931,plain,
mult(X2,rd(true,mult(X1,true))) = rd(X2,rd(rd(mult(X1,mult(X1,X2)),X2),X1)),
inference(step,[status(thm)],[t70930,t1828]) ).
cnf(t37792,plain,
rd(X1,rd(rd(mult(X2,mult(X2,X1)),X1),X2)) = mult(X1,rd(true,mult(X2,true))),
inference(orient,[status(thm)],[t70931]) ).
cnf(t302,plain,
mult(rd(X1,X2),mult(rd(X2,X1),X3)) = X3,
inference(cp,[status(thm)],[t299,t9]) ).
cnf(t353,plain,
mult(rd(X1,X2),mult(rd(X2,X1),X3)) = X3,
inference(orient,[status(thm)],[t302]) ).
cnf(t37815,plain,
mult(X1,rd(true,mult(rd(X2,X2),true))) = rd(X1,rd(rd(X1,X1),rd(X2,X2))),
inference(cp,[status(thm)],[t37792,t353]) ).
cnf(t70932,plain,
mult(X1,rd(X2,X2)) = rd(X1,rd(rd(X1,X1),rd(X2,X2))),
inference(step,[status(thm)],[t37815,t289]) ).
cnf(t38004,plain,
rd(X1,rd(rd(X1,X1),rd(X2,X2))) = mult(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t70932]) ).
cnf(t38031,plain,
X1 = mult(mult(X1,rd(X2,X2)),rd(rd(X1,X1),rd(X2,X2))),
inference(cp,[status(thm)],[t8,t38004]) ).
cnf(t38129,plain,
mult(mult(X1,rd(X2,X2)),rd(rd(X1,X1),rd(X2,X2))) = X1,
inference(orient,[status(thm)],[t38031]) ).
cnf(t38188,plain,
rd(rd(X1,X1),rd(X2,X2)) = ld(mult(X1,rd(X2,X2)),X1),
inference(cp,[status(thm)],[t9,t38129]) ).
cnf(t38310,plain,
ld(mult(X1,rd(X2,X2)),X1) = rd(rd(X1,X1),rd(X2,X2)),
inference(orient,[status(thm)],[t38188]) ).
cnf(t38354,plain,
rd(true,mult(mult(X1,rd(X2,X2)),true)) = rd(rd(rd(X1,X1),rd(X2,X2)),X1),
inference(cp,[status(thm)],[t266,t38310]) ).
cnf(t38458,plain,
rd(rd(rd(X1,X1),rd(X2,X2)),X1) = rd(true,mult(mult(X1,rd(X2,X2)),true)),
inference(orient,[status(thm)],[t38354]) ).
cnf(t840,plain,
ld(rd(X1,mult(X2,X1)),rd(X3,rd(X1,mult(X2,X1)))) = mult(ld(rd(X1,mult(X2,X1)),X3),rd(Y3,ld(X2,Y3))),
inference(cp,[status(thm)],[t818,t322]) ).
cnf(t70674,plain,
mult(rd(mult(X2,X1),X1),rd(X3,rd(X1,mult(X2,X1)))) = mult(ld(rd(X1,mult(X2,X1)),X3),rd(Y3,ld(X2,Y3))),
inference(step,[status(thm)],[t840,t299]) ).
cnf(t70675,plain,
mult(X2,rd(X3,rd(X1,mult(X2,X1)))) = mult(ld(rd(X1,mult(X2,X1)),X3),rd(Y3,ld(X2,Y3))),
inference(step,[status(thm)],[t70674,t12]) ).
cnf(t70676,plain,
mult(X2,rd(X3,rd(X1,mult(X2,X1)))) = mult(mult(rd(mult(X2,X1),X1),X3),rd(Y3,ld(X2,Y3))),
inference(step,[status(thm)],[t70675,t299]) ).
cnf(t70677,plain,
mult(X2,rd(X3,rd(X1,mult(X2,X1)))) = mult(mult(X2,X3),rd(Y3,ld(X2,Y3))),
inference(step,[status(thm)],[t70676,t12]) ).
cnf(t70678,plain,
mult(X2,rd(X3,rd(X1,mult(X2,X1)))) = mult(mult(X2,X3),X2),
inference(step,[status(thm)],[t70677,t24]) ).
cnf(t1989,plain,
mult(X1,rd(X2,rd(X3,mult(X1,X3)))) = mult(mult(X1,X2),X1),
inference(orient,[status(thm)],[t70678]) ).
cnf(t2029,plain,
rd(X1,rd(X2,mult(X3,X2))) = ld(X3,mult(mult(X3,X1),X3)),
inference(cp,[status(thm)],[t9,t1989]) ).
cnf(t21872,plain,
rd(X1,rd(X2,mult(X3,X2))) = ld(X3,mult(mult(X3,X1),X3)),
inference(orient,[status(thm)],[t2029]) ).
cnf(t38461,plain,
rd(true,mult(mult(rd(X1,mult(X2,X1)),rd(X3,X3)),true)) = ld(X2,mult(mult(X2,rd(rd(rd(X1,mult(X2,X1)),rd(X1,mult(X2,X1))),rd(X3,X3))),X2)),
inference(cp,[status(thm)],[t38458,t21872]) ).
cnf(t70933,plain,
rd(true,mult(ld(X2,rd(X3,X3)),true)) = ld(X2,mult(mult(X2,rd(rd(rd(X1,mult(X2,X1)),rd(X1,mult(X2,X1))),rd(X3,X3))),X2)),
inference(step,[status(thm)],[t38461,t322]) ).
cnf(t70934,plain,
rd(true,mult(ld(X2,rd(X3,X3)),true)) = rd(rd(rd(rd(X1,mult(X2,X1)),rd(X1,mult(X2,X1))),rd(X3,X3)),rd(true,mult(X2,true))),
inference(step,[status(thm)],[t70933,t21872]) ).
cnf(t1680,plain,
mult(X1,rd(ld(X1,X2),X3)) = rd(rd(X2,ld(X1,X3)),X1),
inference(cp,[status(thm)],[t1674,t7]) ).
cnf(t1771,plain,
mult(X1,rd(ld(X1,X2),X3)) = rd(rd(X2,ld(X1,X3)),X1),
inference(orient,[status(thm)],[t1680]) ).
cnf(t1776,plain,
rd(rd(X1,ld(rd(X2,mult(X3,X2)),Y3)),rd(X2,mult(X3,X2))) = ld(X3,rd(ld(rd(X2,mult(X3,X2)),X1),Y3)),
inference(cp,[status(thm)],[t1771,t322]) ).
cnf(t70911,plain,
rd(rd(X1,mult(rd(mult(X3,X2),X2),Y3)),rd(X2,mult(X3,X2))) = ld(X3,rd(ld(rd(X2,mult(X3,X2)),X1),Y3)),
inference(step,[status(thm)],[t1776,t299]) ).
cnf(t70912,plain,
rd(rd(X1,mult(X3,Y3)),rd(X2,mult(X3,X2))) = ld(X3,rd(ld(rd(X2,mult(X3,X2)),X1),Y3)),
inference(step,[status(thm)],[t70911,t12]) ).
cnf(t70913,plain,
rd(rd(X1,mult(X3,Y3)),rd(X2,mult(X3,X2))) = ld(X3,rd(mult(rd(mult(X3,X2),X2),X1),Y3)),
inference(step,[status(thm)],[t70912,t299]) ).
cnf(t70914,plain,
rd(rd(X1,mult(X3,Y3)),rd(X2,mult(X3,X2))) = ld(X3,rd(mult(X3,X1),Y3)),
inference(step,[status(thm)],[t70913,t12]) ).
cnf(t30617,plain,
rd(rd(X1,mult(X2,X3)),rd(Y3,mult(X2,Y3))) = ld(X2,rd(mult(X2,X1),X3)),
inference(orient,[status(thm)],[t70914]) ).
cnf(t70935,plain,
rd(true,mult(ld(X2,rd(X3,X3)),true)) = rd(rd(ld(X2,rd(mult(X2,X1),X1)),rd(X3,X3)),rd(true,mult(X2,true))),
inference(step,[status(thm)],[t70934,t30617]) ).
cnf(t1831,plain,
rd(rd(mult(rd(X1,mult(X2,X1)),X3),Y3),rd(X1,mult(X2,X1))) = ld(X2,rd(X3,mult(rd(X1,mult(X2,X1)),Y3))),
inference(cp,[status(thm)],[t1828,t322]) ).
cnf(t70916,plain,
rd(rd(ld(X2,X3),Y3),rd(X1,mult(X2,X1))) = ld(X2,rd(X3,mult(rd(X1,mult(X2,X1)),Y3))),
inference(step,[status(thm)],[t1831,t322]) ).
cnf(t70917,plain,
rd(rd(ld(X2,X3),Y3),rd(X1,mult(X2,X1))) = ld(X2,rd(X3,ld(X2,Y3))),
inference(step,[status(thm)],[t70916,t322]) ).
cnf(t31220,plain,
rd(rd(ld(X1,X2),X3),rd(Y3,mult(X1,Y3))) = ld(X1,rd(X2,ld(X1,X3))),
inference(orient,[status(thm)],[t70917]) ).
cnf(t70936,plain,
rd(true,mult(ld(X2,rd(X3,X3)),true)) = ld(X2,rd(rd(mult(X2,X1),X1),ld(X2,rd(X3,X3)))),
inference(step,[status(thm)],[t70935,t31220]) ).
cnf(t70937,plain,
rd(true,mult(ld(X2,rd(X3,X3)),true)) = ld(X2,rd(X2,ld(X2,rd(X3,X3)))),
inference(step,[status(thm)],[t70936,t12]) ).
cnf(t38555,plain,
ld(X1,rd(X1,ld(X1,rd(X2,X2)))) = rd(true,mult(ld(X1,rd(X2,X2)),true)),
inference(orient,[status(thm)],[t70937]) ).
cnf(t4665,plain,
ld(rd(X1,mult(X2,X1)),ld(ld(rd(X1,mult(X2,X1)),ld(X2,X3)),Y3)) = ld(ld(X2,rd(X3,X2)),mult(rd(X1,mult(X2,X1)),Y3)),
inference(cp,[status(thm)],[t4639,t818]) ).
cnf(t70711,plain,
mult(rd(mult(X2,X1),X1),ld(ld(rd(X1,mult(X2,X1)),ld(X2,X3)),Y3)) = ld(ld(X2,rd(X3,X2)),mult(rd(X1,mult(X2,X1)),Y3)),
inference(step,[status(thm)],[t4665,t299]) ).
cnf(t70712,plain,
mult(X2,ld(ld(rd(X1,mult(X2,X1)),ld(X2,X3)),Y3)) = ld(ld(X2,rd(X3,X2)),mult(rd(X1,mult(X2,X1)),Y3)),
inference(step,[status(thm)],[t70711,t12]) ).
cnf(t70713,plain,
mult(X2,ld(mult(rd(mult(X2,X1),X1),ld(X2,X3)),Y3)) = ld(ld(X2,rd(X3,X2)),mult(rd(X1,mult(X2,X1)),Y3)),
inference(step,[status(thm)],[t70712,t299]) ).
cnf(t70714,plain,
mult(X2,ld(mult(X2,ld(X2,X3)),Y3)) = ld(ld(X2,rd(X3,X2)),mult(rd(X1,mult(X2,X1)),Y3)),
inference(step,[status(thm)],[t70713,t12]) ).
cnf(t70715,plain,
mult(X2,ld(X3,Y3)) = ld(ld(X2,rd(X3,X2)),mult(rd(X1,mult(X2,X1)),Y3)),
inference(step,[status(thm)],[t70714,t7]) ).
cnf(t70716,plain,
mult(X2,ld(X3,Y3)) = ld(ld(X2,rd(X3,X2)),ld(X2,Y3)),
inference(step,[status(thm)],[t70715,t322]) ).
cnf(t4862,plain,
ld(ld(X1,rd(X2,X1)),ld(X1,X3)) = mult(X1,ld(X2,X3)),
inference(orient,[status(thm)],[t70716]) ).
cnf(t4890,plain,
mult(X1,ld(mult(X2,X1),X3)) = ld(ld(X1,X2),ld(X1,X3)),
inference(cp,[status(thm)],[t4862,t12]) ).
cnf(t4936,plain,
ld(ld(X1,X2),ld(X1,X3)) = mult(X1,ld(mult(X2,X1),X3)),
inference(orient,[status(thm)],[t4890]) ).
cnf(t4937,plain,
mult(X1,ld(mult(X2,X1),X2)) = rd(ld(X1,X2),ld(X1,X2)),
inference(cp,[status(thm)],[t4936,t416]) ).
cnf(t4992,plain,
mult(X1,ld(mult(X2,X1),X2)) = rd(ld(X1,X2),ld(X1,X2)),
inference(orient,[status(thm)],[t4937]) ).
cnf(t5042,plain,
ld(mult(X1,X2),X1) = ld(X2,rd(ld(X2,X1),ld(X2,X1))),
inference(cp,[status(thm)],[t9,t4992]) ).
cnf(t5466,plain,
ld(X1,rd(ld(X1,X2),ld(X1,X2))) = ld(mult(X2,X1),X2),
inference(orient,[status(thm)],[t5042]) ).
cnf(t38567,plain,
rd(true,mult(ld(X1,rd(ld(X1,X2),ld(X1,X2))),true)) = ld(X1,rd(X1,ld(mult(X2,X1),X2))),
inference(cp,[status(thm)],[t38555,t5466]) ).
cnf(t70938,plain,
rd(true,mult(ld(mult(X2,X1),X2),true)) = ld(X1,rd(X1,ld(mult(X2,X1),X2))),
inference(step,[status(thm)],[t38567,t5466]) ).
cnf(t38680,plain,
ld(X1,rd(X1,ld(mult(X2,X1),X2))) = rd(true,mult(ld(mult(X2,X1),X2),true)),
inference(orient,[status(thm)],[t70938]) ).
cnf(t38780,plain,
rd(X1,ld(mult(X2,X1),X2)) = mult(X1,rd(true,mult(ld(mult(X2,X1),X2),true))),
inference(cp,[status(thm)],[t7,t38680]) ).
cnf(t69298,plain,
mult(X1,rd(true,mult(ld(mult(X2,X1),X2),true))) = rd(X1,ld(mult(X2,X1),X2)),
inference(orient,[status(thm)],[t38780]) ).
cnf(t69367,plain,
rd(rd(rd(X1,X1),rd(X2,X2)),ld(mult(mult(X1,rd(X2,X2)),rd(rd(X1,X1),rd(X2,X2))),mult(X1,rd(X2,X2)))) = mult(rd(rd(X1,X1),rd(X2,X2)),rd(true,mult(ld(X1,mult(X1,rd(X2,X2))),true))),
inference(cp,[status(thm)],[t69298,t38129]) ).
cnf(t71108,plain,
rd(rd(rd(X1,X1),rd(X2,X2)),ld(X1,mult(X1,rd(X2,X2)))) = mult(rd(rd(X1,X1),rd(X2,X2)),rd(true,mult(ld(X1,mult(X1,rd(X2,X2))),true))),
inference(step,[status(thm)],[t69367,t38129]) ).
cnf(t71109,plain,
rd(rd(rd(X1,X1),rd(X2,X2)),rd(X2,X2)) = mult(rd(rd(X1,X1),rd(X2,X2)),rd(true,mult(ld(X1,mult(X1,rd(X2,X2))),true))),
inference(step,[status(thm)],[t71108,t9]) ).
cnf(t214,plain,
rd(X1,true) = rd(X2,mult(rd(true,X1),X2)),
inference(cp,[status(thm)],[t24,t205]) ).
cnf(t281,plain,
rd(X1,mult(rd(true,X2),X1)) = rd(X2,true),
inference(orient,[status(thm)],[t214]) ).
cnf(t295,plain,
rd(mult(rd(X1,X2),true),true) = rd(X3,mult(rd(X2,X1),X3)),
inference(cp,[status(thm)],[t281,t289]) ).
cnf(t70631,plain,
rd(X1,X2) = rd(X3,mult(rd(X2,X1),X3)),
inference(step,[status(thm)],[t295,t12]) ).
cnf(t312,plain,
rd(X1,mult(rd(X2,X3),X1)) = rd(X3,X2),
inference(orient,[status(thm)],[t70631]) ).
cnf(t317,plain,
rd(X1,mult(X2,X1)) = rd(X3,mult(X2,X3)),
inference(cp,[status(thm)],[t312,t12]) ).
cnf(t547,plain,
rd(X1,mult(X2,X1)) = rd(X3,mult(X2,X3)),
inference(orient,[status(thm)],[t317]) ).
cnf(t2072,plain,
rd(rd(X1,X2),X2) = mult(X1,rd(X3,mult(mult(X2,X2),X3))),
inference(cp,[status(thm)],[t2063,t547]) ).
cnf(t3098,plain,
mult(X1,rd(X2,mult(mult(X3,X3),X2))) = rd(rd(X1,X3),X3),
inference(orient,[status(thm)],[t2072]) ).
cnf(t3128,plain,
rd(rd(X1,rd(X2,X2)),rd(X2,X2)) = mult(X1,rd(X3,mult(rd(rd(X2,X2),rd(X2,X2)),X3))),
inference(cp,[status(thm)],[t3098,t370]) ).
cnf(t70703,plain,
rd(rd(X1,rd(X2,X2)),rd(X2,X2)) = mult(X1,rd(rd(X2,X2),rd(X2,X2))),
inference(step,[status(thm)],[t3128,t312]) ).
cnf(t70704,plain,
rd(rd(X1,rd(X2,X2)),rd(X2,X2)) = mult(X1,rd(X2,X2)),
inference(step,[status(thm)],[t70703,t493]) ).
cnf(t3943,plain,
rd(rd(X1,rd(X2,X2)),rd(X2,X2)) = mult(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t70704]) ).
cnf(t71110,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(rd(X1,X1),rd(X2,X2)),rd(true,mult(ld(X1,mult(X1,rd(X2,X2))),true))),
inference(step,[status(thm)],[t71109,t3943]) ).
cnf(t71111,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(rd(X1,X1),rd(X2,X2)),rd(true,mult(rd(X2,X2),true))),
inference(step,[status(thm)],[t71110,t9]) ).
cnf(t71112,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(rd(X1,X1),rd(X2,X2)),rd(X2,X2)),
inference(step,[status(thm)],[t71111,t289]) ).
cnf(t71113,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(X1,X1),
inference(step,[status(thm)],[t71112,t8]) ).
cnf(t69684,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(X1,X1),
inference(orient,[status(thm)],[t71113]) ).
cnf(t69817,plain,
ld(mult(rd(X1,X1),rd(X2,X2)),X2) = mult(rd(X2,X2),ld(rd(X2,X2),X2)),
inference(cp,[status(thm)],[t47698,t69684]) ).
cnf(t71116,plain,
ld(rd(X1,X1),X2) = mult(rd(X2,X2),ld(rd(X2,X2),X2)),
inference(step,[status(thm)],[t69817,t69684]) ).
cnf(t71117,plain,
mult(rd(X1,X1),X2) = mult(rd(X2,X2),ld(rd(X2,X2),X2)),
inference(step,[status(thm)],[t71116,t299]) ).
cnf(t71118,plain,
mult(rd(X1,X1),X2) = X2,
inference(step,[status(thm)],[t71117,t7]) ).
cnf(t69889,plain,
mult(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t71118]) ).
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(t421,plain,
X1 = rd(X1,rd(X1,X1)),
inference(cp,[status(thm)],[t24,t416]) ).
cnf(t441,plain,
rd(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t421]) ).
cnf(t738,plain,
rd(mult(X1,X2),ld(X1,rd(X2,X2))) = mult(mult(X1,X2),X1),
inference(cp,[status(thm)],[t730,t441]) ).
cnf(t1581,plain,
rd(mult(X1,X2),ld(X1,rd(X2,X2))) = mult(mult(X1,X2),X1),
inference(orient,[status(thm)],[t738]) ).
cnf(t1600,plain,
mult(mult(rd(X1,X2),X2),rd(X1,X2)) = rd(X1,ld(rd(X1,X2),rd(X2,X2))),
inference(cp,[status(thm)],[t1581,t8]) ).
cnf(t70695,plain,
mult(X1,rd(X1,X2)) = rd(X1,ld(rd(X1,X2),rd(X2,X2))),
inference(step,[status(thm)],[t1600,t8]) ).
cnf(t70696,plain,
mult(X1,rd(X1,X2)) = rd(X1,mult(rd(X2,X1),rd(X2,X2))),
inference(step,[status(thm)],[t70695,t299]) ).
cnf(t2892,plain,
rd(X1,mult(rd(X2,X1),rd(X2,X2))) = mult(X1,rd(X1,X2)),
inference(orient,[status(thm)],[t70696]) ).
cnf(t2923,plain,
rd(rd(mult(rd(X1,X2),X2),rd(X1,X1)),rd(X1,X2)) = mult(rd(X1,X2),mult(X2,rd(X2,X1))),
inference(cp,[status(thm)],[t1828,t2892]) ).
cnf(t70701,plain,
rd(rd(X1,rd(X1,X1)),rd(X1,X2)) = mult(rd(X1,X2),mult(X2,rd(X2,X1))),
inference(step,[status(thm)],[t2923,t8]) ).
cnf(t70702,plain,
rd(X1,rd(X1,X2)) = mult(rd(X1,X2),mult(X2,rd(X2,X1))),
inference(step,[status(thm)],[t70701,t441]) ).
cnf(t3679,plain,
mult(rd(X1,X2),mult(X2,rd(X2,X1))) = rd(X1,rd(X1,X2)),
inference(orient,[status(thm)],[t70702]) ).
cnf(t3709,plain,
rd(mult(mult(X1,X1),X2),rd(mult(mult(X1,X1),X2),X2)) = mult(rd(mult(mult(X1,X1),X2),X2),rd(rd(X2,X1),X1)),
inference(cp,[status(thm)],[t3679,t3098]) ).
cnf(t70793,plain,
rd(mult(mult(X1,X1),X2),mult(X1,X1)) = mult(rd(mult(mult(X1,X1),X2),X2),rd(rd(X2,X1),X1)),
inference(step,[status(thm)],[t3709,t12]) ).
cnf(t70794,plain,
rd(mult(mult(X1,X1),X2),mult(X1,X1)) = mult(mult(X1,X1),rd(rd(X2,X1),X1)),
inference(step,[status(thm)],[t70793,t12]) ).
cnf(t12020,plain,
mult(mult(X1,X1),rd(rd(X2,X1),X1)) = rd(mult(mult(X1,X1),X2),mult(X1,X1)),
inference(orient,[status(thm)],[t70794]) ).
cnf(t12089,plain,
rd(mult(mult(X1,X1),mult(X2,X1)),mult(X1,X1)) = mult(mult(X1,X1),rd(X2,X1)),
inference(cp,[status(thm)],[t12020,t12]) ).
cnf(t53816,plain,
rd(mult(mult(X1,X1),mult(X2,X1)),mult(X1,X1)) = mult(mult(X1,X1),rd(X2,X1)),
inference(orient,[status(thm)],[t12089]) ).
cnf(t69951,plain,
mult(mult(rd(X1,X1),rd(X1,X1)),rd(X2,rd(X1,X1))) = rd(mult(rd(X1,X1),mult(X2,rd(X1,X1))),mult(rd(X1,X1),rd(X1,X1))),
inference(cp,[status(thm)],[t53816,t69889]) ).
cnf(t71182,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),rd(X2,rd(X1,X1))) = rd(mult(rd(X1,X1),mult(X2,rd(X1,X1))),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t69951,t370]) ).
cnf(t71183,plain,
mult(rd(X1,X1),rd(X2,rd(X1,X1))) = rd(mult(rd(X1,X1),mult(X2,rd(X1,X1))),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71182,t493]) ).
cnf(t825,plain,
ld(rd(X1,X2),rd(X3,rd(X1,X2))) = mult(mult(rd(X2,X1),X3),rd(Y3,mult(rd(X1,X2),Y3))),
inference(cp,[status(thm)],[t818,t299]) ).
cnf(t70753,plain,
mult(rd(X2,X1),rd(X3,rd(X1,X2))) = mult(mult(rd(X2,X1),X3),rd(Y3,mult(rd(X1,X2),Y3))),
inference(step,[status(thm)],[t825,t299]) ).
cnf(t70754,plain,
mult(rd(X2,X1),rd(X3,rd(X1,X2))) = mult(mult(rd(X2,X1),X3),rd(X2,X1)),
inference(step,[status(thm)],[t70753,t312]) ).
cnf(t67,plain,
mult(mult(rd(X1,X2),X3),rd(X1,X2)) = rd(mult(rd(X1,X2),mult(X3,X1)),X2),
inference(cp,[status(thm)],[t58,t8]) ).
cnf(t8647,plain,
mult(mult(rd(X1,X2),X3),rd(X1,X2)) = rd(mult(rd(X1,X2),mult(X3,X1)),X2),
inference(orient,[status(thm)],[t67]) ).
cnf(t70755,plain,
mult(rd(X2,X1),rd(X3,rd(X1,X2))) = rd(mult(rd(X2,X1),mult(X3,X2)),X1),
inference(step,[status(thm)],[t70754,t8647]) ).
cnf(t9284,plain,
mult(rd(X1,X2),rd(X3,rd(X2,X1))) = rd(mult(rd(X1,X2),mult(X3,X1)),X2),
inference(orient,[status(thm)],[t70755]) ).
cnf(t739,plain,
rd(mult(X1,X2),ld(X1,ld(X3,X2))) = mult(mult(X1,X3),X1),
inference(cp,[status(thm)],[t730,t24]) ).
cnf(t1623,plain,
rd(mult(X1,X2),ld(X1,ld(X3,X2))) = mult(mult(X1,X3),X1),
inference(orient,[status(thm)],[t739]) ).
cnf(t1643,plain,
mult(mult(rd(X1,X2),X3),rd(X1,X2)) = rd(X1,ld(rd(X1,X2),ld(X3,X2))),
inference(cp,[status(thm)],[t1623,t8]) ).
cnf(t70764,plain,
rd(mult(rd(X1,X2),mult(X3,X1)),X2) = rd(X1,ld(rd(X1,X2),ld(X3,X2))),
inference(step,[status(thm)],[t1643,t8647]) ).
cnf(t70765,plain,
rd(mult(rd(X1,X2),mult(X3,X1)),X2) = rd(X1,mult(rd(X2,X1),ld(X3,X2))),
inference(step,[status(thm)],[t70764,t299]) ).
cnf(t10079,plain,
rd(mult(rd(X1,X2),mult(X3,X1)),X2) = rd(X1,mult(rd(X2,X1),ld(X3,X2))),
inference(orient,[status(thm)],[t70765]) ).
cnf(t70768,plain,
mult(rd(X1,X2),rd(X3,rd(X2,X1))) = rd(X1,mult(rd(X2,X1),ld(X3,X2))),
inference(step,[status(thm)],[t9284,t10079]) ).
cnf(t10082,plain,
mult(rd(X1,X2),rd(X3,rd(X2,X1))) = rd(X1,mult(rd(X2,X1),ld(X3,X2))),
inference(orient,[status(thm)],[t70768]) ).
cnf(t71184,plain,
rd(X1,mult(rd(X1,X1),ld(X2,X1))) = rd(mult(rd(X1,X1),mult(X2,rd(X1,X1))),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71183,t10082]) ).
cnf(t71185,plain,
rd(X1,ld(X2,X1)) = rd(mult(rd(X1,X1),mult(X2,rd(X1,X1))),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71184,t69889]) ).
cnf(t71186,plain,
X2 = rd(mult(rd(X1,X1),mult(X2,rd(X1,X1))),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71185,t24]) ).
cnf(t3719,plain,
rd(mult(rd(X1,X2),X3),rd(mult(rd(X1,X2),X3),X3)) = mult(rd(mult(rd(X1,X2),X3),X3),mult(X3,rd(X2,X1))),
inference(cp,[status(thm)],[t3679,t312]) ).
cnf(t70795,plain,
rd(mult(rd(X1,X2),X3),rd(X1,X2)) = mult(rd(mult(rd(X1,X2),X3),X3),mult(X3,rd(X2,X1))),
inference(step,[status(thm)],[t3719,t12]) ).
cnf(t70796,plain,
rd(mult(rd(X1,X2),X3),rd(X1,X2)) = mult(rd(X1,X2),mult(X3,rd(X2,X1))),
inference(step,[status(thm)],[t70795,t12]) ).
cnf(t12167,plain,
mult(rd(X1,X2),mult(X3,rd(X2,X1))) = rd(mult(rd(X1,X2),X3),rd(X1,X2)),
inference(orient,[status(thm)],[t70796]) ).
cnf(t71187,plain,
X2 = rd(rd(mult(rd(X1,X1),X2),rd(X1,X1)),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71186,t12167]) ).
cnf(t71188,plain,
X2 = rd(rd(X2,rd(X1,X1)),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71187,t69889]) ).
cnf(t71189,plain,
X2 = rd(rd(X2,rd(X1,X1)),rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71188,t370]) ).
cnf(t71190,plain,
X2 = rd(rd(X2,rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t71189,t493]) ).
cnf(t71191,plain,
X2 = mult(X2,rd(X1,X1)),
inference(step,[status(thm)],[t71190,t3943]) ).
cnf(t70385,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t71191]) ).
fof(f5,conjecture,
! [X0,X1] :
( mult(ld(X1,X1),X0) = X0
& mult(X0,ld(X1,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f5_neg,negated_conjecture,
~ ! [X0,X1] :
( mult(ld(X1,X1),X0) = X0
& mult(X0,ld(X1,X1)) = X0 ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [X0,X1] :
( mult(ld(X1,X1),X0) != X0
| mult(X0,ld(X1,X1)) != X0 ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( mult(ld(sk1,sk1),sk0) != sk0
| mult(sk0,ld(sk1,sk1)) != sk0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f5_nnf]) ).
cnf(c5,plain,
( mult(ld(sk1,sk1),sk0) != sk0
| mult(sk0,ld(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,ld(sk1,sk1)),sk0,ifeq(mult(ld(sk1,sk1),sk0),sk0,false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(mult(sk0,ld(sk1,sk1)),sk0,ifeq(mult(rd(sk1,sk1),sk0),sk0,false,true),true),
inference(rw,[status(thm)],[g0_0,t416]) ).
cnf(g0_2,plain,
true != ifeq(mult(sk0,rd(sk1,sk1)),sk0,ifeq(mult(rd(sk1,sk1),sk0),sk0,false,true),true),
inference(rw,[status(thm)],[g0_1,t416]) ).
cnf(g0_3,plain,
true != ifeq(mult(sk0,rd(sk1,sk1)),sk0,ifeq(sk0,sk0,false,true),true),
inference(rw,[status(thm)],[g0_2,t69889]) ).
cnf(g0_4,plain,
true != ifeq(mult(sk0,rd(sk1,sk1)),sk0,false,true),
inference(rw,[status(thm)],[g0_3,t11]) ).
cnf(g0_5,plain,
true != ifeq(sk0,sk0,false,true),
inference(rw,[status(thm)],[g0_4,t70385]) ).
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 : GRP654+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 15:29:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.20/3.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.20/3.83 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------