%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP715+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 : n014.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 01:28:16 PM UTC 2026
% Result : Theorem 0.16s 2.50s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 83 ( 78 unt; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 87 ( 2 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,conjecture,
! [X0] :
( mult(mult(X0,op_b),op_a) = X0
& mult(mult(X0,op_a),op_b) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f11_neg,negated_conjecture,
~ ! [X0] :
( mult(mult(X0,op_b),op_a) = X0
& mult(mult(X0,op_a),op_b) = X0 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [X0] :
( mult(mult(X0,op_b),op_a) != X0
| mult(mult(X0,op_a),op_b) != X0 ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( mult(mult(sk0,op_b),op_a) != sk0
| mult(mult(sk0,op_a),op_b) != sk0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f11_nnf]) ).
cnf(c11,plain,
( mult(mult(sk0,op_b),op_a) != sk0
| mult(mult(sk0,op_a),op_b) != sk0 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
ifeq(mult(mult(sk0,op_a),op_b),sk0,ifeq(mult(mult(sk0,op_b),op_a),sk0,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t54,plain,
ifeq(mult(mult(sk0,op_a),op_b),sk0,ifeq(mult(mult(sk0,op_b),op_a),sk0,false,true),true) = true,
inference(orient,[status(thm)],[t12]) ).
fof(f5,axiom,
! [C,B,A] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f5_nnf,plain,
! [C,B,A] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
mult(mult(mult(X2,X1),X0),X1) = mult(X2,mult(mult(X1,X0),X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t11,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t19,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(orient,[status(thm)],[t11]) ).
fof(f6,axiom,
! [B,A] : mult(A,mult(B,B)) = mult(mult(A,B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f6_nnf,plain,
! [B,A] : mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] : mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
mult(X1,mult(X0,X0)) = mult(mult(X1,X0),X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t8,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t17,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t23,plain,
mult(mult(mult(X1,X2),X3),mult(X2,X2)) = mult(mult(X1,mult(mult(X2,X3),X2)),X2),
inference(cp,[status(thm)],[t17,t19]) ).
cnf(t3698,plain,
mult(mult(X1,mult(mult(X2,X3),X2)),X2) = mult(mult(mult(X1,X2),X3),mult(X2,X2)),
inference(orient,[status(thm)],[t23]) ).
fof(f10,axiom,
mult(op_b,op_a) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
fof(f10_nnf,plain,
mult(op_b,op_a) = unit,
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
mult(op_b,op_a) = unit,
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t2,plain,
mult(op_b,op_a) = unit,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t38,plain,
mult(op_b,op_a) = unit,
inference(orient,[status(thm)],[t2]) ).
cnf(t3764,plain,
mult(mult(mult(X1,op_b),op_a),mult(op_b,op_b)) = mult(mult(X1,mult(unit,op_b)),op_b),
inference(cp,[status(thm)],[t3698,t38]) ).
fof(f8,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(f8_nnf,plain,
! [A] : mult(unit,A) = A,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : mult(unit,A) = A,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
mult(unit,X0) = X0,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t3,plain,
mult(unit,X1) = X1,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t14,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t10302,plain,
mult(mult(mult(X1,op_b),op_a),mult(op_b,op_b)) = mult(mult(X1,op_b),op_b),
inference(step,[status(thm)],[t3764,t14]) ).
cnf(t10303,plain,
mult(mult(mult(X1,op_b),op_a),mult(op_b,op_b)) = mult(X1,mult(op_b,op_b)),
inference(step,[status(thm)],[t10302,t17]) ).
cnf(t9261,plain,
mult(mult(mult(X1,op_b),op_a),mult(op_b,op_b)) = mult(X1,mult(op_b,op_b)),
inference(orient,[status(thm)],[t10303]) ).
cnf(t9283,plain,
mult(mult(X1,op_b),mult(mult(op_a,mult(op_b,op_b)),op_a)) = mult(mult(X1,mult(op_b,op_b)),op_a),
inference(cp,[status(thm)],[t19,t9261]) ).
fof(f9,axiom,
mult(op_a,op_b) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f9_nnf,plain,
mult(op_a,op_b) = unit,
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
mult(op_a,op_b) = unit,
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t1,plain,
mult(op_a,op_b) = unit,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t33,plain,
mult(op_a,op_b) = unit,
inference(orient,[status(thm)],[t1]) ).
cnf(t34,plain,
mult(op_a,mult(op_b,op_b)) = mult(unit,op_b),
inference(cp,[status(thm)],[t17,t33]) ).
cnf(t10022,plain,
mult(op_a,mult(op_b,op_b)) = op_b,
inference(step,[status(thm)],[t34,t14]) ).
cnf(t58,plain,
mult(op_a,mult(op_b,op_b)) = op_b,
inference(orient,[status(thm)],[t10022]) ).
cnf(t10304,plain,
mult(mult(X1,op_b),mult(op_b,op_a)) = mult(mult(X1,mult(op_b,op_b)),op_a),
inference(step,[status(thm)],[t9283,t58]) ).
cnf(t10305,plain,
mult(mult(X1,op_b),unit) = mult(mult(X1,mult(op_b,op_b)),op_a),
inference(step,[status(thm)],[t10304,t38]) ).
fof(f7,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f7_nnf,plain,
! [A] : mult(A,unit) = A,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] : mult(A,unit) = A,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
mult(X0,unit) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t0,plain,
mult(X1,unit) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t13,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t10306,plain,
mult(X1,op_b) = mult(mult(X1,mult(op_b,op_b)),op_a),
inference(step,[status(thm)],[t10305,t13]) ).
cnf(t9605,plain,
mult(mult(X1,mult(op_b,op_b)),op_a) = mult(X1,op_b),
inference(orient,[status(thm)],[t10306]) ).
cnf(t9606,plain,
mult(mult(X1,op_a),op_b) = mult(X1,mult(mult(op_a,mult(op_b,op_b)),op_a)),
inference(cp,[status(thm)],[t9605,t19]) ).
cnf(t10307,plain,
mult(mult(X1,op_a),op_b) = mult(X1,mult(op_a,op_b)),
inference(step,[status(thm)],[t9606,t9605]) ).
cnf(t10308,plain,
mult(mult(X1,op_a),op_b) = mult(X1,unit),
inference(step,[status(thm)],[t10307,t33]) ).
cnf(t10309,plain,
mult(mult(X1,op_a),op_b) = X1,
inference(step,[status(thm)],[t10308,t13]) ).
cnf(t9638,plain,
mult(mult(X1,op_a),op_b) = X1,
inference(orient,[status(thm)],[t10309]) ).
cnf(t10310,plain,
ifeq(sk0,sk0,ifeq(mult(mult(sk0,op_b),op_a),sk0,false,true),true) = true,
inference(step,[status(thm)],[t54,t9638]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t10311,plain,
ifeq(mult(mult(sk0,op_b),op_a),sk0,false,true) = true,
inference(step,[status(thm)],[t10310,t16]) ).
cnf(t9673,plain,
ifeq(mult(mult(sk0,op_b),op_a),sk0,false,true) = true,
inference(rw,[status(thm)],[t10311]) ).
cnf(t22,plain,
mult(mult(X1,X2),mult(mult(X2,X3),X2)) = mult(mult(mult(X1,mult(X2,X2)),X3),X2),
inference(cp,[status(thm)],[t19,t17]) ).
cnf(t2232,plain,
mult(mult(mult(X1,mult(X2,X2)),X3),X2) = mult(mult(X1,X2),mult(mult(X2,X3),X2)),
inference(orient,[status(thm)],[t22]) ).
cnf(t9607,plain,
mult(mult(X1,mult(op_a,op_a)),op_b) = mult(mult(X1,op_a),mult(mult(op_a,mult(op_b,op_b)),op_a)),
inference(cp,[status(thm)],[t9605,t2232]) ).
cnf(t10312,plain,
mult(mult(X1,mult(op_a,op_a)),op_b) = mult(mult(X1,op_a),mult(op_a,op_b)),
inference(step,[status(thm)],[t9607,t9605]) ).
cnf(t10313,plain,
mult(mult(X1,mult(op_a,op_a)),op_b) = mult(mult(X1,op_a),unit),
inference(step,[status(thm)],[t10312,t33]) ).
cnf(t10314,plain,
mult(mult(X1,mult(op_a,op_a)),op_b) = mult(X1,op_a),
inference(step,[status(thm)],[t10313,t13]) ).
cnf(t9734,plain,
mult(mult(X1,mult(op_a,op_a)),op_b) = mult(X1,op_a),
inference(orient,[status(thm)],[t10314]) ).
cnf(t9735,plain,
mult(mult(X1,op_b),op_a) = mult(X1,mult(mult(op_b,mult(op_a,op_a)),op_b)),
inference(cp,[status(thm)],[t9734,t19]) ).
cnf(t10315,plain,
mult(mult(X1,op_b),op_a) = mult(X1,mult(op_b,op_a)),
inference(step,[status(thm)],[t9735,t9734]) ).
cnf(t10316,plain,
mult(mult(X1,op_b),op_a) = mult(X1,unit),
inference(step,[status(thm)],[t10315,t38]) ).
cnf(t10317,plain,
mult(mult(X1,op_b),op_a) = X1,
inference(step,[status(thm)],[t10316,t13]) ).
cnf(t9766,plain,
mult(mult(X1,op_b),op_a) = X1,
inference(orient,[status(thm)],[t10317]) ).
cnf(t10320,plain,
ifeq(sk0,sk0,false,true) = true,
inference(step,[status(thm)],[t9673,t9766]) ).
cnf(t10321,plain,
false = true,
inference(step,[status(thm)],[t10320,t16]) ).
cnf(t10021,plain,
false = true,
inference(orient,[status(thm)],[t10321]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t10021]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 15:49:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/2.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------