%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP658+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 : n006.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 01:27:55 PM UTC 2026
% Result : Theorem 5.51s 6.29s
% Output : Proof 5.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 7
% Syntax : Number of formulae : 92 ( 87 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 196 ( 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(t21,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(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]) ).
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(f4,axiom,
! [C,B,A] : mult(mult(A,mult(B,B)),C) = mult(mult(A,B),mult(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [C,B,A] : mult(mult(A,mult(B,B)),C) = mult(mult(A,B),mult(B,C)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : mult(mult(A,mult(B,B)),C) = mult(mult(A,B),mult(B,C)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
mult(mult(X2,mult(X1,X1)),X0) = mult(mult(X2,X1),mult(X1,X0)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(mult(X1,X2),mult(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t14,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(mult(X1,X2),mult(X2,X3)),
inference(orient,[status(thm)],[t5]) ).
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(t16,plain,
mult(mult(rd(X1,mult(X2,X2)),X2),mult(X2,X3)) = mult(X1,X3),
inference(cp,[status(thm)],[t14,t8]) ).
cnf(t54,plain,
mult(mult(rd(X1,mult(X2,X2)),X2),mult(X2,X3)) = mult(X1,X3),
inference(orient,[status(thm)],[t16]) ).
cnf(t58,plain,
mult(X1,ld(X2,X3)) = mult(mult(rd(X1,mult(X2,X2)),X2),X3),
inference(cp,[status(thm)],[t54,t7]) ).
cnf(t70,plain,
mult(mult(rd(X1,mult(X2,X2)),X2),X3) = mult(X1,ld(X2,X3)),
inference(orient,[status(thm)],[t58]) ).
cnf(t77,plain,
mult(mult(mult(rd(X1,mult(X2,X2)),X2),X3),mult(X3,Y3)) = mult(mult(X1,ld(X2,mult(X3,X3))),Y3),
inference(cp,[status(thm)],[t14,t70]) ).
cnf(t838,plain,
mult(mult(X1,ld(X2,X3)),mult(X3,Y3)) = mult(mult(X1,ld(X2,mult(X3,X3))),Y3),
inference(step,[status(thm)],[t77,t70]) ).
cnf(t132,plain,
mult(mult(X1,ld(X2,mult(X3,X3))),Y3) = mult(mult(X1,ld(X2,X3)),mult(X3,Y3)),
inference(orient,[status(thm)],[t838]) ).
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]) ).
cnf(t140,plain,
mult(mult(X1,ld(X2,X2)),mult(X2,X3)) = mult(mult(X1,X2),X3),
inference(cp,[status(thm)],[t132,t12]) ).
cnf(t289,plain,
mult(mult(X1,ld(X2,X2)),mult(X2,X3)) = mult(mult(X1,X2),X3),
inference(orient,[status(thm)],[t140]) ).
cnf(t300,plain,
mult(mult(X1,X2),ld(X2,X3)) = mult(mult(X1,ld(X2,X2)),X3),
inference(cp,[status(thm)],[t289,t7]) ).
cnf(t319,plain,
mult(mult(X1,ld(X2,X2)),X3) = mult(mult(X1,X2),ld(X2,X3)),
inference(orient,[status(thm)],[t300]) ).
cnf(t335,plain,
mult(X1,ld(X2,X2)) = rd(mult(mult(X1,X2),ld(X2,X3)),X3),
inference(cp,[status(thm)],[t10,t319]) ).
cnf(t437,plain,
rd(mult(mult(X1,X2),ld(X2,X3)),X3) = mult(X1,ld(X2,X2)),
inference(orient,[status(thm)],[t335]) ).
cnf(t328,plain,
mult(mult(rd(X1,ld(X2,X2)),X2),ld(X2,X3)) = mult(X1,X3),
inference(cp,[status(thm)],[t319,t8]) ).
cnf(t637,plain,
mult(mult(rd(X1,ld(X2,X2)),X2),ld(X2,X3)) = mult(X1,X3),
inference(orient,[status(thm)],[t328]) ).
cnf(t136,plain,
mult(mult(X1,ld(X1,X2)),mult(X2,X3)) = mult(mult(X2,X2),X3),
inference(cp,[status(thm)],[t132,t7]) ).
cnf(t839,plain,
mult(X2,mult(X2,X3)) = mult(mult(X2,X2),X3),
inference(step,[status(thm)],[t136,t7]) ).
cnf(t164,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(orient,[status(thm)],[t839]) ).
cnf(t174,plain,
mult(X1,X1) = rd(mult(X1,mult(X1,X2)),X2),
inference(cp,[status(thm)],[t10,t164]) ).
cnf(t190,plain,
rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1),
inference(orient,[status(thm)],[t174]) ).
cnf(t202,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(cp,[status(thm)],[t190,t8]) ).
cnf(t244,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(orient,[status(thm)],[t202]) ).
cnf(t260,plain,
rd(X1,X2) = ld(rd(X1,X2),rd(mult(rd(X1,X2),X1),X2)),
inference(cp,[status(thm)],[t12,t244]) ).
cnf(t196,plain,
mult(X1,X1) = rd(mult(X1,X2),ld(X1,X2)),
inference(cp,[status(thm)],[t190,t7]) ).
cnf(t208,plain,
rd(mult(X1,X2),ld(X1,X2)) = mult(X1,X1),
inference(orient,[status(thm)],[t196]) ).
cnf(t215,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(X1,ld(rd(X1,X2),X2)),
inference(cp,[status(thm)],[t208,t8]) ).
cnf(t841,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,ld(rd(X1,X2),X2)),
inference(step,[status(thm)],[t215,t244]) ).
cnf(t273,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,ld(rd(X1,X2),X2)),
inference(orient,[status(thm)],[t841]) ).
cnf(t844,plain,
rd(X1,X2) = ld(rd(X1,X2),rd(X1,ld(rd(X1,X2),X2))),
inference(step,[status(thm)],[t260,t273]) ).
cnf(t556,plain,
ld(rd(X1,X2),rd(X1,ld(rd(X1,X2),X2))) = rd(X1,X2),
inference(orient,[status(thm)],[t844]) ).
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]) ).
cnf(t571,plain,
rd(X1,X1) = ld(rd(X1,X1),rd(X1,X1)),
inference(cp,[status(thm)],[t556,t23]) ).
cnf(t595,plain,
ld(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t571]) ).
cnf(t646,plain,
mult(X1,X2) = mult(mult(rd(X1,rd(X3,X3)),rd(X3,X3)),ld(rd(X3,X3),X2)),
inference(cp,[status(thm)],[t637,t595]) ).
cnf(t846,plain,
mult(X1,X2) = mult(X1,ld(rd(X3,X3),X2)),
inference(step,[status(thm)],[t646,t8]) ).
cnf(t674,plain,
mult(X1,ld(rd(X2,X2),X3)) = mult(X1,X3),
inference(orient,[status(thm)],[t846]) ).
cnf(t675,plain,
mult(rd(X1,X1),X2) = X2,
inference(cp,[status(thm)],[t674,t7]) ).
cnf(t709,plain,
mult(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t675]) ).
cnf(t717,plain,
mult(rd(X1,X1),ld(X2,X2)) = rd(mult(X2,ld(X2,X3)),X3),
inference(cp,[status(thm)],[t437,t709]) ).
cnf(t852,plain,
ld(X2,X2) = rd(mult(X2,ld(X2,X3)),X3),
inference(step,[status(thm)],[t717,t709]) ).
cnf(t853,plain,
ld(X2,X2) = rd(X3,X3),
inference(step,[status(thm)],[t852,t7]) ).
cnf(t764,plain,
ld(X1,X1) = rd(X2,X2),
inference(orient,[status(thm)],[t853]) ).
cnf(t775,plain,
X1 = mult(X1,rd(X2,X2)),
inference(cp,[status(thm)],[t7,t764]) ).
cnf(t809,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t775]) ).
cnf(t832,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)],[t21,t809]) ).
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(t866,plain,
true = ifeq(mult(rd(X1,X1),sk0(rd(X1,X1))),sk0(rd(X1,X1)),false,true),
inference(step,[status(thm)],[t832,t9]) ).
cnf(t867,plain,
true = ifeq(sk0(rd(X1,X1)),sk0(rd(X1,X1)),false,true),
inference(step,[status(thm)],[t866,t709]) ).
cnf(t868,plain,
true = false,
inference(step,[status(thm)],[t867,t9]) ).
cnf(t836,plain,
false = true,
inference(orient,[status(thm)],[t868]) ).
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,t836]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP658+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n006.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 15:31:38 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.51/6.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.51/6.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------