%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:27:56 PM UTC 2026
% Result : Theorem 0.14s 5.94s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 7
% Syntax : Number of formulae : 124 ( 119 unt; 0 def)
% Number of atoms : 129 ( 128 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 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 : 7 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 259 ( 2 sgn 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f5_neg,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
! [X0] :
? [X1] :
( mult(X0,X1) != X1
| mult(X1,X0) != X1 ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
! [X0] :
( mult(X0,sk0(X0)) != sk0(X0)
| mult(sk0(X0),X0) != sk0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f5_nnf]) ).
cnf(c5,plain,
( mult(X0,sk0(X0)) != sk0(X0)
| mult(sk0(X0),X0) != sk0(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t6,plain,
ifeq(mult(sk0(X1),X1),sk0(X1),ifeq(mult(X1,sk0(X1)),sk0(X1),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t22,plain,
ifeq(mult(sk0(X1),X1),sk0(X1),ifeq(mult(X1,sk0(X1)),sk0(X1),false,true),true) = true,
inference(orient,[status(thm)],[t6]) ).
fof(f3,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/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(t10,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
fof(f0,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/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(t11,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t10,t7]) ).
cnf(t23,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t11]) ).
fof(f1,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/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(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [C,B,A] : mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
mult(mult(X2,mult(X1,X0)),X1) = mult(mult(X2,X1),mult(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
mult(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),mult(X3,X2)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t14,plain,
mult(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),mult(X3,X2)),
inference(orient,[status(thm)],[t5]) ).
cnf(t16,plain,
mult(mult(X1,X2),mult(ld(X2,X3),X2)) = mult(mult(X1,X3),X2),
inference(cp,[status(thm)],[t14,t7]) ).
cnf(t25,plain,
mult(mult(X1,X2),mult(ld(X2,X3),X2)) = mult(mult(X1,X3),X2),
inference(orient,[status(thm)],[t16]) ).
cnf(t30,plain,
mult(ld(X1,X2),X1) = ld(mult(X3,X1),mult(mult(X3,X2),X1)),
inference(cp,[status(thm)],[t12,t25]) ).
cnf(t123,plain,
ld(mult(X1,X2),mult(mult(X1,X3),X2)) = mult(ld(X2,X3),X2),
inference(orient,[status(thm)],[t30]) ).
cnf(t136,plain,
mult(ld(X1,ld(X2,X3)),X1) = ld(mult(X2,X1),mult(X3,X1)),
inference(cp,[status(thm)],[t123,t7]) ).
cnf(t145,plain,
ld(mult(X1,X2),mult(X3,X2)) = mult(ld(X2,ld(X1,X3)),X2),
inference(orient,[status(thm)],[t136]) ).
fof(f2,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/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(t153,plain,
mult(ld(X1,ld(rd(X2,X1),X3)),X1) = ld(X2,mult(X3,X1)),
inference(cp,[status(thm)],[t145,t8]) ).
cnf(t211,plain,
mult(ld(X1,ld(rd(X2,X1),X3)),X1) = ld(X2,mult(X3,X1)),
inference(orient,[status(thm)],[t153]) ).
cnf(t222,plain,
ld(X1,ld(rd(X2,X1),X3)) = rd(ld(X2,mult(X3,X1)),X1),
inference(cp,[status(thm)],[t10,t211]) ).
cnf(t232,plain,
ld(X1,ld(rd(X2,X1),X3)) = rd(ld(X2,mult(X3,X1)),X1),
inference(orient,[status(thm)],[t222]) ).
cnf(t239,plain,
ld(rd(X1,X2),X3) = mult(X2,rd(ld(X1,mult(X3,X2)),X2)),
inference(cp,[status(thm)],[t7,t232]) ).
cnf(t379,plain,
mult(X1,rd(ld(X2,mult(X3,X1)),X1)) = ld(rd(X2,X1),X3),
inference(orient,[status(thm)],[t239]) ).
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(t380,plain,
ld(rd(rd(mult(X1,X2),X3),X2),X1) = mult(X2,rd(X3,X2)),
inference(cp,[status(thm)],[t379,t24]) ).
cnf(t407,plain,
ld(rd(rd(mult(X1,X2),X3),X2),X1) = mult(X2,rd(X3,X2)),
inference(orient,[status(thm)],[t380]) ).
cnf(t28,plain,
mult(mult(rd(X1,X2),X3),X2) = mult(X1,mult(ld(X2,X3),X2)),
inference(cp,[status(thm)],[t25,t8]) ).
cnf(t35,plain,
mult(mult(rd(X1,X2),X3),X2) = mult(X1,mult(ld(X2,X3),X2)),
inference(orient,[status(thm)],[t28]) ).
cnf(t37,plain,
mult(X1,mult(ld(X2,X2),X2)) = mult(X1,X2),
inference(cp,[status(thm)],[t35,t8]) ).
cnf(t45,plain,
mult(X1,mult(ld(X2,X2),X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t37]) ).
cnf(t49,plain,
mult(ld(X1,X1),X1) = ld(X2,mult(X2,X1)),
inference(cp,[status(thm)],[t12,t45]) ).
cnf(t973,plain,
mult(ld(X1,X1),X1) = X1,
inference(step,[status(thm)],[t49,t12]) ).
cnf(t58,plain,
mult(ld(X1,X1),X1) = X1,
inference(orient,[status(thm)],[t973]) ).
cnf(t60,plain,
ld(X1,X1) = rd(X1,X1),
inference(cp,[status(thm)],[t10,t58]) ).
cnf(t64,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t60]) ).
cnf(t146,plain,
mult(ld(X1,ld(X2,X2)),X1) = rd(mult(X2,X1),mult(X2,X1)),
inference(cp,[status(thm)],[t145,t64]) ).
cnf(t974,plain,
mult(ld(X1,rd(X2,X2)),X1) = rd(mult(X2,X1),mult(X2,X1)),
inference(step,[status(thm)],[t146,t64]) ).
cnf(t165,plain,
mult(ld(X1,rd(X2,X2)),X1) = rd(mult(X2,X1),mult(X2,X1)),
inference(orient,[status(thm)],[t974]) ).
cnf(t172,plain,
ld(X1,rd(X2,X2)) = rd(rd(mult(X2,X1),mult(X2,X1)),X1),
inference(cp,[status(thm)],[t10,t165]) ).
cnf(t277,plain,
rd(rd(mult(X1,X2),mult(X1,X2)),X2) = ld(X2,rd(X1,X1)),
inference(orient,[status(thm)],[t172]) ).
cnf(t408,plain,
mult(X1,rd(mult(X2,X1),X1)) = ld(ld(X1,rd(X2,X2)),X2),
inference(cp,[status(thm)],[t407,t277]) ).
cnf(t978,plain,
mult(X1,X2) = ld(ld(X1,rd(X2,X2)),X2),
inference(step,[status(thm)],[t408,t10]) ).
cnf(t428,plain,
ld(ld(X1,rd(X2,X2)),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t978]) ).
cnf(t434,plain,
ld(X1,rd(X2,X2)) = rd(X2,mult(X1,X2)),
inference(cp,[status(thm)],[t23,t428]) ).
cnf(t441,plain,
ld(X1,rd(X2,X2)) = rd(X2,mult(X1,X2)),
inference(orient,[status(thm)],[t434]) ).
cnf(t19,plain,
mult(X1,mult(X2,X3)) = rd(mult(mult(X1,X2),mult(X3,X2)),X2),
inference(cp,[status(thm)],[t10,t14]) ).
cnf(t73,plain,
rd(mult(mult(X1,X2),mult(X3,X2)),X2) = mult(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t19]) ).
cnf(t86,plain,
mult(X1,mult(X2,rd(X3,X2))) = rd(mult(mult(X1,X2),X3),X2),
inference(cp,[status(thm)],[t73,t8]) ).
cnf(t105,plain,
mult(X1,mult(X2,rd(X3,X2))) = rd(mult(mult(X1,X2),X3),X2),
inference(orient,[status(thm)],[t86]) ).
cnf(t113,plain,
mult(X1,rd(X2,X1)) = ld(X3,rd(mult(mult(X3,X1),X2),X1)),
inference(cp,[status(thm)],[t12,t105]) ).
cnf(t193,plain,
ld(X1,rd(mult(mult(X1,X2),X3),X2)) = mult(X2,rd(X3,X2)),
inference(orient,[status(thm)],[t113]) ).
cnf(t197,plain,
mult(X1,rd(ld(mult(X2,X1),X3),X1)) = ld(X2,rd(X3,X1)),
inference(cp,[status(thm)],[t193,t7]) ).
cnf(t300,plain,
mult(X1,rd(ld(mult(X2,X1),X3),X1)) = ld(X2,rd(X3,X1)),
inference(orient,[status(thm)],[t197]) ).
cnf(t311,plain,
ld(rd(X1,X2),rd(X3,X2)) = mult(X2,rd(ld(X1,X3),X2)),
inference(cp,[status(thm)],[t300,t8]) ).
cnf(t328,plain,
ld(rd(X1,X2),rd(X3,X2)) = mult(X2,rd(ld(X1,X3),X2)),
inference(orient,[status(thm)],[t311]) ).
cnf(t446,plain,
rd(X1,mult(rd(X2,X1),X1)) = mult(X1,rd(ld(X2,X1),X1)),
inference(cp,[status(thm)],[t441,t328]) ).
cnf(t984,plain,
rd(X1,X2) = mult(X1,rd(ld(X2,X1),X1)),
inference(step,[status(thm)],[t446,t8]) ).
cnf(t470,plain,
mult(X1,rd(ld(X2,X1),X1)) = rd(X1,X2),
inference(orient,[status(thm)],[t984]) ).
cnf(t478,plain,
rd(X1,rd(X1,X2)) = mult(X1,rd(X2,X1)),
inference(cp,[status(thm)],[t470,t24]) ).
cnf(t498,plain,
mult(X1,rd(X2,X1)) = rd(X1,rd(X1,X2)),
inference(orient,[status(thm)],[t478]) ).
cnf(t509,plain,
rd(X1,rd(X1,mult(X2,X1))) = mult(X1,X2),
inference(cp,[status(thm)],[t498,t10]) ).
cnf(t562,plain,
rd(X1,rd(X1,mult(X2,X1))) = mult(X1,X2),
inference(orient,[status(thm)],[t509]) ).
cnf(t448,plain,
rd(X1,X1) = mult(X2,rd(X1,mult(X2,X1))),
inference(cp,[status(thm)],[t7,t441]) ).
cnf(t531,plain,
mult(X1,rd(X2,mult(X1,X2))) = rd(X2,X2),
inference(orient,[status(thm)],[t448]) ).
cnf(t537,plain,
rd(X1,X1) = mult(rd(X2,X1),rd(X1,X2)),
inference(cp,[status(thm)],[t531,t8]) ).
cnf(t630,plain,
mult(rd(X1,X2),rd(X2,X1)) = rd(X2,X2),
inference(orient,[status(thm)],[t537]) ).
cnf(t646,plain,
rd(X1,X2) = rd(rd(X2,X2),rd(X2,X1)),
inference(cp,[status(thm)],[t10,t630]) ).
cnf(t790,plain,
rd(rd(X1,X1),rd(X1,X2)) = rd(X2,X1),
inference(orient,[status(thm)],[t646]) ).
cnf(t574,plain,
rd(X1,mult(X2,X1)) = ld(mult(X1,X2),X1),
inference(cp,[status(thm)],[t24,t562]) ).
cnf(t580,plain,
ld(mult(X1,X2),X1) = rd(X1,mult(X2,X1)),
inference(orient,[status(thm)],[t574]) ).
cnf(t583,plain,
rd(X1,mult(ld(X1,X2),X1)) = ld(X2,X1),
inference(cp,[status(thm)],[t580,t7]) ).
cnf(t657,plain,
rd(X1,mult(ld(X1,X2),X1)) = ld(X2,X1),
inference(orient,[status(thm)],[t583]) ).
cnf(t791,plain,
rd(mult(ld(X1,X2),X1),X1) = rd(rd(X1,X1),ld(X2,X1)),
inference(cp,[status(thm)],[t790,t657]) ).
cnf(t1000,plain,
ld(X1,X2) = rd(rd(X1,X1),ld(X2,X1)),
inference(step,[status(thm)],[t791,t10]) ).
cnf(t886,plain,
rd(rd(X1,X1),ld(X2,X1)) = ld(X1,X2),
inference(orient,[status(thm)],[t1000]) ).
cnf(t887,plain,
ld(rd(X1,X1),X2) = rd(rd(X1,X1),ld(X2,rd(X1,X1))),
inference(cp,[status(thm)],[t886,t790]) ).
cnf(t1001,plain,
ld(rd(X1,X1),X2) = X2,
inference(step,[status(thm)],[t887,t23]) ).
cnf(t909,plain,
ld(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t1001]) ).
cnf(t916,plain,
mult(rd(X1,X1),X2) = X2,
inference(cp,[status(thm)],[t909,t12]) ).
cnf(t928,plain,
mult(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t916]) ).
cnf(t938,plain,
mult(X1,rd(X2,X2)) = rd(X1,rd(X1,X1)),
inference(cp,[status(thm)],[t562,t928]) ).
cnf(t66,plain,
X1 = rd(X1,rd(X1,X1)),
inference(cp,[status(thm)],[t23,t64]) ).
cnf(t71,plain,
rd(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t66]) ).
cnf(t1002,plain,
mult(X1,rd(X2,X2)) = X1,
inference(step,[status(thm)],[t938,t71]) ).
cnf(t952,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t1002]) ).
cnf(t966,plain,
true = ifeq(sk0(rd(X1,X1)),sk0(rd(X1,X1)),ifeq(mult(rd(X1,X1),sk0(rd(X1,X1))),sk0(rd(X1,X1)),false,true),true),
inference(cp,[status(thm)],[t22,t952]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t1003,plain,
true = ifeq(mult(rd(X1,X1),sk0(rd(X1,X1))),sk0(rd(X1,X1)),false,true),
inference(step,[status(thm)],[t966,t9]) ).
cnf(t1004,plain,
true = ifeq(sk0(rd(X1,X1)),sk0(rd(X1,X1)),false,true),
inference(step,[status(thm)],[t1003,t928]) ).
cnf(t1005,plain,
true = false,
inference(step,[status(thm)],[t1004,t9]) ).
cnf(t971,plain,
false = true,
inference(orient,[status(thm)],[t1005]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t971]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n003.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 15:33:09 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/5.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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