%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP656+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 : 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 01:27:55 PM UTC 2026
% Result : Theorem 6.02s 1.21s
% Output : Proof 6.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 55 unt; 0 def)
% Number of atoms : 65 ( 64 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 : 125 ( 2 sgn 31 !; 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(f4,axiom,
! [C,B,A] : mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [C,B,A] : mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
mult(mult(X2,X1),mult(X0,X2)) = mult(mult(X2,mult(X1,X0)),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
mult(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),mult(X3,X1)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t14,plain,
mult(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),mult(X3,X1)),
inference(orient,[status(thm)],[t5]) ).
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(t16,plain,
mult(mult(X1,X2),mult(ld(X2,X3),X1)) = mult(mult(X1,X3),X1),
inference(cp,[status(thm)],[t14,t7]) ).
cnf(t25,plain,
mult(mult(X1,X2),mult(ld(X2,X3),X1)) = mult(mult(X1,X3),X1),
inference(orient,[status(thm)],[t16]) ).
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(t26,plain,
mult(mult(X1,X2),X1) = mult(X3,mult(ld(ld(X1,X3),X2),X1)),
inference(cp,[status(thm)],[t25,t7]) ).
cnf(t89,plain,
mult(X1,mult(ld(ld(X2,X1),X3),X2)) = mult(mult(X2,X3),X2),
inference(orient,[status(thm)],[t26]) ).
cnf(t92,plain,
mult(ld(ld(X1,X2),X3),X1) = ld(X2,mult(mult(X1,X3),X1)),
inference(cp,[status(thm)],[t12,t89]) ).
cnf(t102,plain,
ld(X1,mult(mult(X2,X3),X2)) = mult(ld(ld(X2,X1),X3),X2),
inference(orient,[status(thm)],[t92]) ).
cnf(t103,plain,
mult(ld(ld(X1,mult(X1,X2)),X2),X1) = X1,
inference(cp,[status(thm)],[t102,t12]) ).
cnf(t159,plain,
mult(ld(X2,X2),X1) = X1,
inference(step,[status(thm)],[t103,t12]) ).
cnf(t119,plain,
mult(ld(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t159]) ).
cnf(t136,plain,
mult(mult(ld(X1,X1),X2),ld(X1,X1)) = mult(X3,mult(ld(X3,X2),ld(X1,X1))),
inference(cp,[status(thm)],[t25,t119]) ).
cnf(t160,plain,
mult(X2,ld(X1,X1)) = mult(X3,mult(ld(X3,X2),ld(X1,X1))),
inference(step,[status(thm)],[t136,t119]) ).
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]) ).
cnf(t19,plain,
mult(X1,mult(X2,X3)) = rd(mult(mult(X1,X2),mult(X3,X1)),X1),
inference(cp,[status(thm)],[t10,t14]) ).
cnf(t49,plain,
rd(mult(mult(X1,X2),mult(X3,X1)),X1) = mult(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t19]) ).
cnf(t50,plain,
mult(X1,mult(ld(X1,X2),X3)) = rd(mult(X2,mult(X3,X1)),X1),
inference(cp,[status(thm)],[t49,t7]) ).
cnf(t62,plain,
mult(X1,mult(ld(X1,X2),X3)) = rd(mult(X2,mult(X3,X1)),X1),
inference(orient,[status(thm)],[t50]) ).
cnf(t161,plain,
mult(X2,ld(X1,X1)) = rd(mult(X2,mult(ld(X1,X1),X3)),X3),
inference(step,[status(thm)],[t160,t62]) ).
cnf(t162,plain,
mult(X2,ld(X1,X1)) = rd(mult(X2,X3),X3),
inference(step,[status(thm)],[t161,t119]) ).
cnf(t163,plain,
mult(X2,ld(X1,X1)) = X2,
inference(step,[status(thm)],[t162,t10]) ).
cnf(t146,plain,
mult(X1,ld(X2,X2)) = X1,
inference(orient,[status(thm)],[t163]) ).
cnf(t156,plain,
true = ifeq(sk0(ld(X1,X1)),sk0(ld(X1,X1)),ifeq(mult(ld(X1,X1),sk0(ld(X1,X1))),sk0(ld(X1,X1)),false,true),true),
inference(cp,[status(thm)],[t22,t146]) ).
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(t164,plain,
true = ifeq(mult(ld(X1,X1),sk0(ld(X1,X1))),sk0(ld(X1,X1)),false,true),
inference(step,[status(thm)],[t156,t9]) ).
cnf(t165,plain,
true = ifeq(sk0(ld(X1,X1)),sk0(ld(X1,X1)),false,true),
inference(step,[status(thm)],[t164,t119]) ).
cnf(t166,plain,
true = false,
inference(step,[status(thm)],[t165,t9]) ).
cnf(t157,plain,
false = true,
inference(orient,[status(thm)],[t166]) ).
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,t157]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP656+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/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 15:30:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.02/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.02/1.21 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------