%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP654+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 : n015.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 47.73s 6.59s
% Output : Proof 47.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 137
% Number of leaves : 7
% Syntax : Number of formulae : 333 ( 328 unt; 0 def)
% Number of atoms : 338 ( 337 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 13 ~; 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(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]) ).
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]) ).
cnf(t42,plain,
ld(X1,X2) = ld(mult(X3,X1),mult(X1,mult(ld(X1,X3),X2))),
inference(cp,[status(thm)],[t12,t35]) ).
cnf(t4546,plain,
ld(mult(X1,X2),mult(X2,mult(ld(X2,X1),X3))) = ld(X2,X3),
inference(orient,[status(thm)],[t42]) ).
cnf(t4599,plain,
ld(X1,ld(ld(X1,X2),X3)) = ld(mult(X2,X1),mult(X1,X3)),
inference(cp,[status(thm)],[t4546,t7]) ).
cnf(t4638,plain,
ld(mult(X1,X2),mult(X2,X3)) = ld(X2,ld(ld(X2,X1),X3)),
inference(orient,[status(thm)],[t4599]) ).
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(t4711,plain,
ld(rd(X1,X2),ld(ld(rd(X1,X2),X3),X2)) = ld(mult(X3,rd(X1,X2)),X1),
inference(cp,[status(thm)],[t4638,t8]) ).
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]) ).
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]) ).
cnf(t76,plain,
mult(ld(X1,rd(X2,X1)),X3) = ld(X1,mult(X2,ld(X1,X3))),
inference(cp,[status(thm)],[t12,t69]) ).
cnf(t85,plain,
ld(X1,mult(X2,ld(X1,X3))) = mult(ld(X1,rd(X2,X1)),X3),
inference(orient,[status(thm)],[t76]) ).
cnf(t86,plain,
mult(ld(X1,rd(X1,X1)),X2) = ld(X1,X2),
inference(cp,[status(thm)],[t85,t12]) ).
cnf(t97,plain,
mult(ld(X1,rd(X1,X1)),X2) = ld(X1,X2),
inference(orient,[status(thm)],[t86]) ).
cnf(t103,plain,
ld(X1,rd(X1,X1)) = rd(ld(X1,X2),X2),
inference(cp,[status(thm)],[t9,t97]) ).
cnf(t130,plain,
ld(X1,rd(X1,X1)) = rd(ld(X1,X2),X2),
inference(orient,[status(thm)],[t103]) ).
cnf(t143,plain,
ld(X1,X2) = mult(ld(X1,rd(X1,X1)),X2),
inference(cp,[status(thm)],[t8,t130]) ).
cnf(t70637,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)],[t70637]) ).
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(t168,plain,
ld(rd(true,X1),X2) = mult(rd(X1,true),X2),
inference(cp,[status(thm)],[t163,t24]) ).
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(t70638,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)],[t70638]) ).
cnf(t196,plain,
mult(rd(true,X1),X2) = ld(rd(X1,true),X2),
inference(cp,[status(thm)],[t192,t24]) ).
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,t9]) ).
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)],[t9,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,t24]) ).
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(t70640,plain,
mult(rd(X1,X2),X3) = ld(rd(X2,X1),X3),
inference(step,[status(thm)],[t292,t9]) ).
cnf(t299,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(orient,[status(thm)],[t70640]) ).
cnf(t70989,plain,
mult(rd(X2,X1),ld(ld(rd(X1,X2),X3),X2)) = ld(mult(X3,rd(X1,X2)),X1),
inference(step,[status(thm)],[t4711,t299]) ).
cnf(t70990,plain,
mult(rd(X2,X1),ld(mult(rd(X2,X1),X3),X2)) = ld(mult(X3,rd(X1,X2)),X1),
inference(step,[status(thm)],[t70989,t299]) ).
cnf(t47707,plain,
mult(rd(X1,X2),ld(mult(rd(X1,X2),X3),X1)) = ld(mult(X3,rd(X2,X1)),X2),
inference(orient,[status(thm)],[t70990]) ).
cnf(t31,plain,
mult(ld(X1,X2),mult(X1,X3)) = ld(X1,mult(mult(X2,X1),X3)),
inference(cp,[status(thm)],[t12,t25]) ).
cnf(t47,plain,
ld(X1,mult(mult(X2,X1),X3)) = mult(ld(X1,X2),mult(X1,X3)),
inference(orient,[status(thm)],[t31]) ).
cnf(t54,plain,
mult(ld(X1,rd(X2,X1)),mult(X1,X3)) = ld(X1,mult(X2,X3)),
inference(cp,[status(thm)],[t47,t8]) ).
cnf(t560,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)],[t9,t560]) ).
cnf(t1421,plain,
rd(ld(X1,mult(X2,X3)),mult(X1,X3)) = ld(X1,rd(X2,X1)),
inference(orient,[status(thm)],[t583]) ).
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,t12]) ).
cnf(t220,plain,
mult(X1,rd(X2,mult(X1,X2))) = rd(X1,X1),
inference(orient,[status(thm)],[t150]) ).
cnf(t232,plain,
X1 = rd(rd(X1,X1),rd(X2,mult(X1,X2))),
inference(cp,[status(thm)],[t9,t220]) ).
cnf(t341,plain,
rd(rd(X1,X1),rd(X2,mult(X1,X2))) = X1,
inference(orient,[status(thm)],[t232]) ).
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(t70642,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(t70643,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)],[t70642,t9]) ).
cnf(t304,plain,
mult(rd(X1,mult(X2,X1)),X3) = ld(X2,X3),
inference(cp,[status(thm)],[t299,t9]) ).
cnf(t322,plain,
mult(rd(X1,mult(X2,X1)),X3) = ld(X2,X3),
inference(orient,[status(thm)],[t304]) ).
cnf(t70644,plain,
mult(rd(X1,X1),mult(X1,X3)) = ld(X1,mult(ld(rd(X2,mult(X1,X2)),X1),X3)),
inference(step,[status(thm)],[t70643,t322]) ).
cnf(t70645,plain,
mult(rd(X1,X1),mult(X1,X3)) = ld(X1,mult(mult(rd(mult(X1,X2),X2),X1),X3)),
inference(step,[status(thm)],[t70644,t299]) ).
cnf(t70646,plain,
mult(rd(X1,X1),mult(X1,X3)) = mult(ld(X1,rd(mult(X1,X2),X2)),mult(X1,X3)),
inference(step,[status(thm)],[t70645,t47]) ).
cnf(t70647,plain,
mult(rd(X1,X1),mult(X1,X3)) = mult(ld(X1,X1),mult(X1,X3)),
inference(step,[status(thm)],[t70646,t9]) ).
cnf(t390,plain,
mult(ld(X1,X1),mult(X1,X2)) = mult(rd(X1,X1),mult(X1,X2)),
inference(orient,[status(thm)],[t70647]) ).
cnf(t405,plain,
ld(X1,X1) = rd(mult(rd(X1,X1),mult(X1,X2)),mult(X1,X2)),
inference(cp,[status(thm)],[t9,t390]) ).
cnf(t70648,plain,
ld(X1,X1) = rd(X1,X1),
inference(step,[status(thm)],[t405,t9]) ).
cnf(t416,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t70648]) ).
cnf(t418,plain,
X1 = mult(X1,rd(X1,X1)),
inference(cp,[status(thm)],[t7,t416]) ).
cnf(t424,plain,
mult(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t418]) ).
cnf(t1432,plain,
ld(X1,rd(X2,X1)) = rd(ld(X1,X2),mult(X1,rd(X2,X2))),
inference(cp,[status(thm)],[t1421,t424]) ).
cnf(t2631,plain,
rd(ld(X1,X2),mult(X1,rd(X2,X2))) = ld(X1,rd(X2,X1)),
inference(orient,[status(thm)],[t1432]) ).
cnf(t2638,plain,
ld(X1,rd(mult(X1,X2),X1)) = rd(X2,mult(X1,rd(mult(X1,X2),mult(X1,X2)))),
inference(cp,[status(thm)],[t2631,t12]) ).
cnf(t15,plain,
mult(X1,mult(X2,mult(X1,ld(mult(mult(X1,X2),X1),X3)))) = X3,
inference(cp,[status(thm)],[t14,t7]) ).
cnf(t634,plain,
mult(X1,mult(X2,mult(X1,ld(mult(mult(X1,X2),X1),X3)))) = X3,
inference(orient,[status(thm)],[t15]) ).
cnf(t19,plain,
mult(mult(X1,X2),X1) = rd(mult(X1,mult(X2,mult(X1,X3))),X3),
inference(cp,[status(thm)],[t9,t14]) ).
cnf(t58,plain,
rd(mult(X1,mult(X2,mult(X1,X3))),X3) = mult(mult(X1,X2),X1),
inference(orient,[status(thm)],[t19]) ).
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(t70658,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(t70659,plain,
mult(ld(X2,X3),rd(X1,mult(X2,X1))) = rd(ld(X2,mult(X3,ld(X2,Y3))),Y3),
inference(step,[status(thm)],[t70658,t322]) ).
cnf(t70660,plain,
mult(ld(X2,X3),rd(X1,mult(X2,X1))) = rd(mult(ld(X2,rd(X3,X2)),Y3),Y3),
inference(step,[status(thm)],[t70659,t85]) ).
cnf(t70661,plain,
mult(ld(X2,X3),rd(X1,mult(X2,X1))) = ld(X2,rd(X3,X2)),
inference(step,[status(thm)],[t70660,t9]) ).
cnf(t817,plain,
mult(ld(X1,X2),rd(X3,mult(X1,X3))) = ld(X1,rd(X2,X1)),
inference(orient,[status(thm)],[t70661]) ).
cnf(t853,plain,
mult(X1,ld(X2,rd(X3,mult(X2,X3)))) = mult(X2,ld(X2,rd(rd(X1,X2),X2))),
inference(cp,[status(thm)],[t69,t817]) ).
cnf(t422,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(X1,mult(X2,rd(X1,X1))),
inference(cp,[status(thm)],[t85,t416]) ).
cnf(t494,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(t497,plain,
mult(ld(X1,rd(rd(X1,X1),X1)),X1) = ld(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(cp,[status(thm)],[t494,t370]) ).
cnf(t419,plain,
rd(true,mult(X1,true)) = rd(rd(X1,X1),X1),
inference(cp,[status(thm)],[t266,t416]) ).
cnf(t448,plain,
rd(rd(X1,X1),X1) = rd(true,mult(X1,true)),
inference(orient,[status(thm)],[t419]) ).
cnf(t70664,plain,
mult(ld(X1,rd(true,mult(X1,true))),X1) = ld(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t497,t448]) ).
cnf(t420,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(mult(X2,X1),rd(X1,X1)),
inference(cp,[status(thm)],[t35,t416]) ).
cnf(t451,plain,
mult(mult(X1,X2),rd(X2,X2)) = mult(X2,mult(ld(X2,X1),X2)),
inference(orient,[status(thm)],[t420]) ).
cnf(t453,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)],[t451,t424]) ).
cnf(t70649,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)],[t453,t299]) ).
cnf(t70650,plain,
mult(rd(X1,X1),mult(X1,rd(X1,X1))) = mult(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t70649,t8]) ).
cnf(t70651,plain,
mult(rd(X1,X1),X1) = mult(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t70650,t424]) ).
cnf(t70652,plain,
X1 = mult(X1,rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t70651,t8]) ).
cnf(t474,plain,
mult(X1,rd(rd(X1,X1),rd(X1,X1))) = X1,
inference(orient,[status(thm)],[t70652]) ).
cnf(t479,plain,
rd(rd(X1,X1),rd(X1,X1)) = ld(X1,X1),
inference(cp,[status(thm)],[t12,t474]) ).
cnf(t70653,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(step,[status(thm)],[t479,t416]) ).
cnf(t492,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t70653]) ).
cnf(t70665,plain,
mult(ld(X1,rd(true,mult(X1,true))),X1) = ld(X1,rd(X1,X1)),
inference(step,[status(thm)],[t70664,t492]) ).
cnf(t70639,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)],[t70639]) ).
cnf(t274,plain,
ld(X1,rd(X1,X1)) = rd(true,mult(X1,true)),
inference(orient,[status(thm)],[t273]) ).
cnf(t70666,plain,
mult(ld(X1,rd(true,mult(X1,true))),X1) = rd(true,mult(X1,true)),
inference(step,[status(thm)],[t70665,t274]) ).
cnf(t1086,plain,
mult(ld(X1,rd(true,mult(X1,true))),X1) = rd(true,mult(X1,true)),
inference(orient,[status(thm)],[t70666]) ).
cnf(t1095,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)],[t1086,t322]) ).
cnf(t70667,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)],[t1095,t289]) ).
cnf(t70668,plain,
X2 = mult(ld(rd(X1,mult(X2,X1)),rd(true,ld(X2,true))),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t70667,t9]) ).
cnf(t70669,plain,
X2 = mult(mult(rd(mult(X2,X1),X1),rd(true,ld(X2,true))),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t70668,t299]) ).
cnf(t70670,plain,
X2 = mult(mult(X2,rd(true,ld(X2,true))),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t70669,t9]) ).
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(t70671,plain,
X2 = mult(mult(X2,X2),rd(X1,mult(X2,X1))),
inference(step,[status(thm)],[t70670,t23]) ).
cnf(t1120,plain,
mult(mult(X1,X1),rd(X2,mult(X1,X2))) = X1,
inference(orient,[status(thm)],[t70671]) ).
cnf(t1150,plain,
mult(X1,X1) = rd(X1,rd(X2,mult(X1,X2))),
inference(cp,[status(thm)],[t9,t1120]) ).
cnf(t1166,plain,
rd(X1,rd(X2,mult(X1,X2))) = mult(X1,X1),
inference(orient,[status(thm)],[t1150]) ).
cnf(t1188,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)],[t1166,t322]) ).
cnf(t70672,plain,
ld(X2,rd(X1,mult(X2,X1))) = rd(rd(X1,mult(X2,X1)),rd(X3,ld(X2,X3))),
inference(step,[status(thm)],[t1188,t322]) ).
cnf(t70673,plain,
ld(X2,rd(X1,mult(X2,X1))) = rd(rd(X1,mult(X2,X1)),X2),
inference(step,[status(thm)],[t70672,t23]) ).
cnf(t1263,plain,
ld(X1,rd(X2,mult(X1,X2))) = rd(rd(X2,mult(X1,X2)),X1),
inference(orient,[status(thm)],[t70673]) ).
cnf(t1149,plain,
rd(X1,mult(X2,X1)) = ld(mult(X2,X2),X2),
inference(cp,[status(thm)],[t12,t1120]) ).
cnf(t1292,plain,
rd(X1,mult(X2,X1)) = ld(mult(X2,X2),X2),
inference(orient,[status(thm)],[t1149]) ).
cnf(t1330,plain,
rd(true,mult(mult(X1,X1),true)) = rd(rd(X2,mult(X1,X2)),X1),
inference(cp,[status(thm)],[t266,t1292]) ).
cnf(t1337,plain,
rd(rd(X1,mult(X2,X1)),X2) = rd(true,mult(mult(X2,X2),true)),
inference(orient,[status(thm)],[t1330]) ).
cnf(t70674,plain,
ld(X1,rd(X2,mult(X1,X2))) = rd(true,mult(mult(X1,X1),true)),
inference(step,[status(thm)],[t1263,t1337]) ).
cnf(t1338,plain,
ld(X1,rd(X2,mult(X1,X2))) = rd(true,mult(mult(X1,X1),true)),
inference(orient,[status(thm)],[t70674]) ).
cnf(t70687,plain,
mult(X1,rd(true,mult(mult(X2,X2),true))) = mult(X2,ld(X2,rd(rd(X1,X2),X2))),
inference(step,[status(thm)],[t853,t1338]) ).
cnf(t70688,plain,
mult(X1,rd(true,mult(mult(X2,X2),true))) = rd(rd(X1,X2),X2),
inference(step,[status(thm)],[t70687,t7]) ).
cnf(t2062,plain,
mult(X1,rd(true,mult(mult(X2,X2),true))) = rd(rd(X1,X2),X2),
inference(orient,[status(thm)],[t70688]) ).
cnf(t2090,plain,
rd(true,mult(mult(X1,X1),true)) = ld(X2,rd(rd(X2,X1),X1)),
inference(cp,[status(thm)],[t12,t2062]) ).
cnf(t2134,plain,
ld(X1,rd(rd(X1,X2),X2)) = rd(true,mult(mult(X2,X2),true)),
inference(orient,[status(thm)],[t2090]) ).
cnf(t2146,plain,
rd(true,mult(mult(X1,X1),true)) = ld(mult(X2,X1),rd(X2,X1)),
inference(cp,[status(thm)],[t2134,t9]) ).
cnf(t2191,plain,
ld(mult(X1,X2),rd(X1,X2)) = rd(true,mult(mult(X2,X2),true)),
inference(orient,[status(thm)],[t2146]) ).
cnf(t2245,plain,
rd(mult(X1,X2),X1) = mult(X1,mult(X2,mult(X1,rd(true,mult(mult(X1,X1),true))))),
inference(cp,[status(thm)],[t634,t2191]) ).
cnf(t70706,plain,
rd(mult(X1,X2),X1) = mult(X1,mult(X2,rd(rd(X1,X1),X1))),
inference(step,[status(thm)],[t2245,t2062]) ).
cnf(t70707,plain,
rd(mult(X1,X2),X1) = mult(X1,mult(X2,rd(true,mult(X1,true)))),
inference(step,[status(thm)],[t70706,t448]) ).
cnf(t3227,plain,
mult(X1,mult(X2,rd(true,mult(X1,true)))) = rd(mult(X1,X2),X1),
inference(orient,[status(thm)],[t70707]) ).
cnf(t3255,plain,
mult(X1,rd(true,mult(X2,true))) = ld(X2,rd(mult(X2,X1),X2)),
inference(cp,[status(thm)],[t12,t3227]) ).
cnf(t3298,plain,
ld(X1,rd(mult(X1,X2),X1)) = mult(X2,rd(true,mult(X1,true))),
inference(orient,[status(thm)],[t3255]) ).
cnf(t70938,plain,
mult(X2,rd(true,mult(X1,true))) = rd(X2,mult(X1,rd(mult(X1,X2),mult(X1,X2)))),
inference(step,[status(thm)],[t2638,t3298]) ).
cnf(t62,plain,
mult(mult(X1,rd(X2,mult(X1,X3))),X1) = rd(mult(X1,X2),X3),
inference(cp,[status(thm)],[t58,t8]) ).
cnf(t594,plain,
mult(mult(X1,rd(X2,mult(X1,X3))),X1) = rd(mult(X1,X2),X3),
inference(orient,[status(thm)],[t62]) ).
cnf(t602,plain,
rd(mult(X1,X2),ld(X1,X3)) = mult(mult(X1,rd(X2,X3)),X1),
inference(cp,[status(thm)],[t594,t7]) ).
cnf(t729,plain,
mult(mult(X1,rd(X2,X3)),X1) = rd(mult(X1,X2),ld(X1,X3)),
inference(orient,[status(thm)],[t602]) ).
cnf(t752,plain,
mult(X1,rd(X2,X3)) = rd(rd(mult(X1,X2),ld(X1,X3)),X1),
inference(cp,[status(thm)],[t9,t729]) ).
cnf(t1673,plain,
rd(rd(mult(X1,X2),ld(X1,X3)),X1) = mult(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t752]) ).
cnf(t1705,plain,
mult(X1,rd(X2,mult(X1,X3))) = rd(rd(mult(X1,X2),X3),X1),
inference(cp,[status(thm)],[t1673,t12]) ).
cnf(t1827,plain,
mult(X1,rd(X2,mult(X1,X3))) = rd(rd(mult(X1,X2),X3),X1),
inference(orient,[status(thm)],[t1705]) ).
cnf(t70939,plain,
mult(X2,rd(true,mult(X1,true))) = rd(X2,rd(rd(mult(X1,mult(X1,X2)),X2),X1)),
inference(step,[status(thm)],[t70938,t1827]) ).
cnf(t37801,plain,
rd(X1,rd(rd(mult(X2,mult(X2,X1)),X1),X2)) = mult(X1,rd(true,mult(X2,true))),
inference(orient,[status(thm)],[t70939]) ).
cnf(t302,plain,
mult(rd(X1,X2),mult(rd(X2,X1),X3)) = X3,
inference(cp,[status(thm)],[t299,t12]) ).
cnf(t353,plain,
mult(rd(X1,X2),mult(rd(X2,X1),X3)) = X3,
inference(orient,[status(thm)],[t302]) ).
cnf(t37824,plain,
mult(X1,rd(true,mult(rd(X2,X2),true))) = rd(X1,rd(rd(X1,X1),rd(X2,X2))),
inference(cp,[status(thm)],[t37801,t353]) ).
cnf(t70940,plain,
mult(X1,rd(X2,X2)) = rd(X1,rd(rd(X1,X1),rd(X2,X2))),
inference(step,[status(thm)],[t37824,t289]) ).
cnf(t38013,plain,
rd(X1,rd(rd(X1,X1),rd(X2,X2))) = mult(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t70940]) ).
cnf(t38040,plain,
X1 = mult(mult(X1,rd(X2,X2)),rd(rd(X1,X1),rd(X2,X2))),
inference(cp,[status(thm)],[t8,t38013]) ).
cnf(t38138,plain,
mult(mult(X1,rd(X2,X2)),rd(rd(X1,X1),rd(X2,X2))) = X1,
inference(orient,[status(thm)],[t38040]) ).
cnf(t38197,plain,
rd(rd(X1,X1),rd(X2,X2)) = ld(mult(X1,rd(X2,X2)),X1),
inference(cp,[status(thm)],[t12,t38138]) ).
cnf(t38319,plain,
ld(mult(X1,rd(X2,X2)),X1) = rd(rd(X1,X1),rd(X2,X2)),
inference(orient,[status(thm)],[t38197]) ).
cnf(t38363,plain,
rd(true,mult(mult(X1,rd(X2,X2)),true)) = rd(rd(rd(X1,X1),rd(X2,X2)),X1),
inference(cp,[status(thm)],[t266,t38319]) ).
cnf(t38467,plain,
rd(rd(rd(X1,X1),rd(X2,X2)),X1) = rd(true,mult(mult(X1,rd(X2,X2)),true)),
inference(orient,[status(thm)],[t38363]) ).
cnf(t839,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)],[t817,t322]) ).
cnf(t70682,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)],[t839,t299]) ).
cnf(t70683,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)],[t70682,t9]) ).
cnf(t70684,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)],[t70683,t299]) ).
cnf(t70685,plain,
mult(X2,rd(X3,rd(X1,mult(X2,X1)))) = mult(mult(X2,X3),rd(Y3,ld(X2,Y3))),
inference(step,[status(thm)],[t70684,t9]) ).
cnf(t70686,plain,
mult(X2,rd(X3,rd(X1,mult(X2,X1)))) = mult(mult(X2,X3),X2),
inference(step,[status(thm)],[t70685,t23]) ).
cnf(t1988,plain,
mult(X1,rd(X2,rd(X3,mult(X1,X3)))) = mult(mult(X1,X2),X1),
inference(orient,[status(thm)],[t70686]) ).
cnf(t2027,plain,
rd(X1,rd(X2,mult(X3,X2))) = ld(X3,mult(mult(X3,X1),X3)),
inference(cp,[status(thm)],[t12,t1988]) ).
cnf(t21881,plain,
rd(X1,rd(X2,mult(X3,X2))) = ld(X3,mult(mult(X3,X1),X3)),
inference(orient,[status(thm)],[t2027]) ).
cnf(t38470,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)],[t38467,t21881]) ).
cnf(t70941,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)],[t38470,t322]) ).
cnf(t70942,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)],[t70941,t21881]) ).
cnf(t1679,plain,
mult(X1,rd(ld(X1,X2),X3)) = rd(rd(X2,ld(X1,X3)),X1),
inference(cp,[status(thm)],[t1673,t7]) ).
cnf(t1770,plain,
mult(X1,rd(ld(X1,X2),X3)) = rd(rd(X2,ld(X1,X3)),X1),
inference(orient,[status(thm)],[t1679]) ).
cnf(t1775,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)],[t1770,t322]) ).
cnf(t70919,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)],[t1775,t299]) ).
cnf(t70920,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)],[t70919,t9]) ).
cnf(t70921,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)],[t70920,t299]) ).
cnf(t70922,plain,
rd(rd(X1,mult(X3,Y3)),rd(X2,mult(X3,X2))) = ld(X3,rd(mult(X3,X1),Y3)),
inference(step,[status(thm)],[t70921,t9]) ).
cnf(t30626,plain,
rd(rd(X1,mult(X2,X3)),rd(Y3,mult(X2,Y3))) = ld(X2,rd(mult(X2,X1),X3)),
inference(orient,[status(thm)],[t70922]) ).
cnf(t70943,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)],[t70942,t30626]) ).
cnf(t1830,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)],[t1827,t322]) ).
cnf(t70924,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)],[t1830,t322]) ).
cnf(t70925,plain,
rd(rd(ld(X2,X3),Y3),rd(X1,mult(X2,X1))) = ld(X2,rd(X3,ld(X2,Y3))),
inference(step,[status(thm)],[t70924,t322]) ).
cnf(t31229,plain,
rd(rd(ld(X1,X2),X3),rd(Y3,mult(X1,Y3))) = ld(X1,rd(X2,ld(X1,X3))),
inference(orient,[status(thm)],[t70925]) ).
cnf(t70944,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)],[t70943,t31229]) ).
cnf(t70945,plain,
rd(true,mult(ld(X2,rd(X3,X3)),true)) = ld(X2,rd(X2,ld(X2,rd(X3,X3)))),
inference(step,[status(thm)],[t70944,t9]) ).
cnf(t38564,plain,
ld(X1,rd(X1,ld(X1,rd(X2,X2)))) = rd(true,mult(ld(X1,rd(X2,X2)),true)),
inference(orient,[status(thm)],[t70945]) ).
cnf(t4664,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)],[t4638,t817]) ).
cnf(t70719,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)],[t4664,t299]) ).
cnf(t70720,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)],[t70719,t9]) ).
cnf(t70721,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)],[t70720,t299]) ).
cnf(t70722,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)],[t70721,t9]) ).
cnf(t70723,plain,
mult(X2,ld(X3,Y3)) = ld(ld(X2,rd(X3,X2)),mult(rd(X1,mult(X2,X1)),Y3)),
inference(step,[status(thm)],[t70722,t7]) ).
cnf(t70724,plain,
mult(X2,ld(X3,Y3)) = ld(ld(X2,rd(X3,X2)),ld(X2,Y3)),
inference(step,[status(thm)],[t70723,t322]) ).
cnf(t4861,plain,
ld(ld(X1,rd(X2,X1)),ld(X1,X3)) = mult(X1,ld(X2,X3)),
inference(orient,[status(thm)],[t70724]) ).
cnf(t4889,plain,
mult(X1,ld(mult(X2,X1),X3)) = ld(ld(X1,X2),ld(X1,X3)),
inference(cp,[status(thm)],[t4861,t9]) ).
cnf(t4935,plain,
ld(ld(X1,X2),ld(X1,X3)) = mult(X1,ld(mult(X2,X1),X3)),
inference(orient,[status(thm)],[t4889]) ).
cnf(t4936,plain,
mult(X1,ld(mult(X2,X1),X2)) = rd(ld(X1,X2),ld(X1,X2)),
inference(cp,[status(thm)],[t4935,t416]) ).
cnf(t4991,plain,
mult(X1,ld(mult(X2,X1),X2)) = rd(ld(X1,X2),ld(X1,X2)),
inference(orient,[status(thm)],[t4936]) ).
cnf(t5040,plain,
ld(mult(X1,X2),X1) = ld(X2,rd(ld(X2,X1),ld(X2,X1))),
inference(cp,[status(thm)],[t12,t4991]) ).
cnf(t5465,plain,
ld(X1,rd(ld(X1,X2),ld(X1,X2))) = ld(mult(X2,X1),X2),
inference(orient,[status(thm)],[t5040]) ).
cnf(t38576,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)],[t38564,t5465]) ).
cnf(t70946,plain,
rd(true,mult(ld(mult(X2,X1),X2),true)) = ld(X1,rd(X1,ld(mult(X2,X1),X2))),
inference(step,[status(thm)],[t38576,t5465]) ).
cnf(t38689,plain,
ld(X1,rd(X1,ld(mult(X2,X1),X2))) = rd(true,mult(ld(mult(X2,X1),X2),true)),
inference(orient,[status(thm)],[t70946]) ).
cnf(t38789,plain,
rd(X1,ld(mult(X2,X1),X2)) = mult(X1,rd(true,mult(ld(mult(X2,X1),X2),true))),
inference(cp,[status(thm)],[t7,t38689]) ).
cnf(t69307,plain,
mult(X1,rd(true,mult(ld(mult(X2,X1),X2),true))) = rd(X1,ld(mult(X2,X1),X2)),
inference(orient,[status(thm)],[t38789]) ).
cnf(t69376,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)],[t69307,t38138]) ).
cnf(t71116,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)],[t69376,t38138]) ).
cnf(t71117,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)],[t71116,t12]) ).
cnf(t214,plain,
rd(X1,true) = rd(X2,mult(rd(true,X1),X2)),
inference(cp,[status(thm)],[t23,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(t70641,plain,
rd(X1,X2) = rd(X3,mult(rd(X2,X1),X3)),
inference(step,[status(thm)],[t295,t9]) ).
cnf(t312,plain,
rd(X1,mult(rd(X2,X3),X1)) = rd(X3,X2),
inference(orient,[status(thm)],[t70641]) ).
cnf(t317,plain,
rd(X1,mult(X2,X1)) = rd(X3,mult(X2,X3)),
inference(cp,[status(thm)],[t312,t9]) ).
cnf(t546,plain,
rd(X1,mult(X2,X1)) = rd(X3,mult(X2,X3)),
inference(orient,[status(thm)],[t317]) ).
cnf(t2071,plain,
rd(rd(X1,X2),X2) = mult(X1,rd(X3,mult(mult(X2,X2),X3))),
inference(cp,[status(thm)],[t2062,t546]) ).
cnf(t3097,plain,
mult(X1,rd(X2,mult(mult(X3,X3),X2))) = rd(rd(X1,X3),X3),
inference(orient,[status(thm)],[t2071]) ).
cnf(t3127,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)],[t3097,t370]) ).
cnf(t70711,plain,
rd(rd(X1,rd(X2,X2)),rd(X2,X2)) = mult(X1,rd(rd(X2,X2),rd(X2,X2))),
inference(step,[status(thm)],[t3127,t312]) ).
cnf(t70712,plain,
rd(rd(X1,rd(X2,X2)),rd(X2,X2)) = mult(X1,rd(X2,X2)),
inference(step,[status(thm)],[t70711,t492]) ).
cnf(t3942,plain,
rd(rd(X1,rd(X2,X2)),rd(X2,X2)) = mult(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t70712]) ).
cnf(t71118,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)],[t71117,t3942]) ).
cnf(t71119,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)],[t71118,t12]) ).
cnf(t71120,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(rd(X1,X1),rd(X2,X2)),rd(X2,X2)),
inference(step,[status(thm)],[t71119,t289]) ).
cnf(t71121,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(X1,X1),
inference(step,[status(thm)],[t71120,t8]) ).
cnf(t69693,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(X1,X1),
inference(orient,[status(thm)],[t71121]) ).
cnf(t69826,plain,
ld(mult(rd(X1,X1),rd(X2,X2)),X2) = mult(rd(X2,X2),ld(rd(X2,X2),X2)),
inference(cp,[status(thm)],[t47707,t69693]) ).
cnf(t71124,plain,
ld(rd(X1,X1),X2) = mult(rd(X2,X2),ld(rd(X2,X2),X2)),
inference(step,[status(thm)],[t69826,t69693]) ).
cnf(t71125,plain,
mult(rd(X1,X1),X2) = mult(rd(X2,X2),ld(rd(X2,X2),X2)),
inference(step,[status(thm)],[t71124,t299]) ).
cnf(t71126,plain,
mult(rd(X1,X1),X2) = X2,
inference(step,[status(thm)],[t71125,t7]) ).
cnf(t69898,plain,
mult(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t71126]) ).
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)],[t23,t416]) ).
cnf(t440,plain,
rd(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t421]) ).
cnf(t737,plain,
rd(mult(X1,X2),ld(X1,rd(X2,X2))) = mult(mult(X1,X2),X1),
inference(cp,[status(thm)],[t729,t440]) ).
cnf(t1580,plain,
rd(mult(X1,X2),ld(X1,rd(X2,X2))) = mult(mult(X1,X2),X1),
inference(orient,[status(thm)],[t737]) ).
cnf(t1599,plain,
mult(mult(rd(X1,X2),X2),rd(X1,X2)) = rd(X1,ld(rd(X1,X2),rd(X2,X2))),
inference(cp,[status(thm)],[t1580,t8]) ).
cnf(t70703,plain,
mult(X1,rd(X1,X2)) = rd(X1,ld(rd(X1,X2),rd(X2,X2))),
inference(step,[status(thm)],[t1599,t8]) ).
cnf(t70704,plain,
mult(X1,rd(X1,X2)) = rd(X1,mult(rd(X2,X1),rd(X2,X2))),
inference(step,[status(thm)],[t70703,t299]) ).
cnf(t2891,plain,
rd(X1,mult(rd(X2,X1),rd(X2,X2))) = mult(X1,rd(X1,X2)),
inference(orient,[status(thm)],[t70704]) ).
cnf(t2922,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)],[t1827,t2891]) ).
cnf(t70709,plain,
rd(rd(X1,rd(X1,X1)),rd(X1,X2)) = mult(rd(X1,X2),mult(X2,rd(X2,X1))),
inference(step,[status(thm)],[t2922,t8]) ).
cnf(t70710,plain,
rd(X1,rd(X1,X2)) = mult(rd(X1,X2),mult(X2,rd(X2,X1))),
inference(step,[status(thm)],[t70709,t440]) ).
cnf(t3678,plain,
mult(rd(X1,X2),mult(X2,rd(X2,X1))) = rd(X1,rd(X1,X2)),
inference(orient,[status(thm)],[t70710]) ).
cnf(t3708,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)],[t3678,t3097]) ).
cnf(t70801,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)],[t3708,t9]) ).
cnf(t70802,plain,
rd(mult(mult(X1,X1),X2),mult(X1,X1)) = mult(mult(X1,X1),rd(rd(X2,X1),X1)),
inference(step,[status(thm)],[t70801,t9]) ).
cnf(t12029,plain,
mult(mult(X1,X1),rd(rd(X2,X1),X1)) = rd(mult(mult(X1,X1),X2),mult(X1,X1)),
inference(orient,[status(thm)],[t70802]) ).
cnf(t12098,plain,
rd(mult(mult(X1,X1),mult(X2,X1)),mult(X1,X1)) = mult(mult(X1,X1),rd(X2,X1)),
inference(cp,[status(thm)],[t12029,t9]) ).
cnf(t53825,plain,
rd(mult(mult(X1,X1),mult(X2,X1)),mult(X1,X1)) = mult(mult(X1,X1),rd(X2,X1)),
inference(orient,[status(thm)],[t12098]) ).
cnf(t69960,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)],[t53825,t69898]) ).
cnf(t71192,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)],[t69960,t370]) ).
cnf(t71193,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)],[t71192,t492]) ).
cnf(t824,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)],[t817,t299]) ).
cnf(t70761,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)],[t824,t299]) ).
cnf(t70762,plain,
mult(rd(X2,X1),rd(X3,rd(X1,X2))) = mult(mult(rd(X2,X1),X3),rd(X2,X1)),
inference(step,[status(thm)],[t70761,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(t8656,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(t70763,plain,
mult(rd(X2,X1),rd(X3,rd(X1,X2))) = rd(mult(rd(X2,X1),mult(X3,X2)),X1),
inference(step,[status(thm)],[t70762,t8656]) ).
cnf(t9293,plain,
mult(rd(X1,X2),rd(X3,rd(X2,X1))) = rd(mult(rd(X1,X2),mult(X3,X1)),X2),
inference(orient,[status(thm)],[t70763]) ).
cnf(t738,plain,
rd(mult(X1,X2),ld(X1,ld(X3,X2))) = mult(mult(X1,X3),X1),
inference(cp,[status(thm)],[t729,t23]) ).
cnf(t1622,plain,
rd(mult(X1,X2),ld(X1,ld(X3,X2))) = mult(mult(X1,X3),X1),
inference(orient,[status(thm)],[t738]) ).
cnf(t1642,plain,
mult(mult(rd(X1,X2),X3),rd(X1,X2)) = rd(X1,ld(rd(X1,X2),ld(X3,X2))),
inference(cp,[status(thm)],[t1622,t8]) ).
cnf(t70772,plain,
rd(mult(rd(X1,X2),mult(X3,X1)),X2) = rd(X1,ld(rd(X1,X2),ld(X3,X2))),
inference(step,[status(thm)],[t1642,t8656]) ).
cnf(t70773,plain,
rd(mult(rd(X1,X2),mult(X3,X1)),X2) = rd(X1,mult(rd(X2,X1),ld(X3,X2))),
inference(step,[status(thm)],[t70772,t299]) ).
cnf(t10088,plain,
rd(mult(rd(X1,X2),mult(X3,X1)),X2) = rd(X1,mult(rd(X2,X1),ld(X3,X2))),
inference(orient,[status(thm)],[t70773]) ).
cnf(t70776,plain,
mult(rd(X1,X2),rd(X3,rd(X2,X1))) = rd(X1,mult(rd(X2,X1),ld(X3,X2))),
inference(step,[status(thm)],[t9293,t10088]) ).
cnf(t10091,plain,
mult(rd(X1,X2),rd(X3,rd(X2,X1))) = rd(X1,mult(rd(X2,X1),ld(X3,X2))),
inference(orient,[status(thm)],[t70776]) ).
cnf(t71194,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)],[t71193,t10091]) ).
cnf(t71195,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)],[t71194,t69898]) ).
cnf(t71196,plain,
X2 = rd(mult(rd(X1,X1),mult(X2,rd(X1,X1))),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71195,t23]) ).
cnf(t3718,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)],[t3678,t312]) ).
cnf(t70803,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)],[t3718,t9]) ).
cnf(t70804,plain,
rd(mult(rd(X1,X2),X3),rd(X1,X2)) = mult(rd(X1,X2),mult(X3,rd(X2,X1))),
inference(step,[status(thm)],[t70803,t9]) ).
cnf(t12176,plain,
mult(rd(X1,X2),mult(X3,rd(X2,X1))) = rd(mult(rd(X1,X2),X3),rd(X1,X2)),
inference(orient,[status(thm)],[t70804]) ).
cnf(t71197,plain,
X2 = rd(rd(mult(rd(X1,X1),X2),rd(X1,X1)),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71196,t12176]) ).
cnf(t71198,plain,
X2 = rd(rd(X2,rd(X1,X1)),mult(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71197,t69898]) ).
cnf(t71199,plain,
X2 = rd(rd(X2,rd(X1,X1)),rd(rd(X1,X1),rd(X1,X1))),
inference(step,[status(thm)],[t71198,t370]) ).
cnf(t71200,plain,
X2 = rd(rd(X2,rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t71199,t492]) ).
cnf(t71201,plain,
X2 = mult(X2,rd(X1,X1)),
inference(step,[status(thm)],[t71200,t3942]) ).
cnf(t70395,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t71201]) ).
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(sk0,sk0,false,true),true),
inference(rw,[status(thm)],[g0_0,t69898]) ).
cnf(g0_2,plain,
true != ifeq(mult(sk0,rd(sk1,sk1)),sk0,false,true),
inference(rw,[status(thm)],[g0_1,t11]) ).
cnf(g0_3,plain,
true != ifeq(sk0,sk0,false,true),
inference(rw,[status(thm)],[g0_2,t70395]) ).
cnf(g0_4,plain,
true != false,
inference(rw,[status(thm)],[g0_3,t11]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP654+2 : 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 : n015.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 15:33:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 47.73/6.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.73/6.59 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------