%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 01:25:16 PM UTC 2026
% Result : Unsatisfiable 40.52s 16.16s
% Output : Proof 40.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 12
% Syntax : Number of formulae : 115 ( 31 unt; 0 def)
% Number of atoms : 496 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 469 ( 88 ~; 381 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 91 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f16,axiom,
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f16_nnf,plain,
! [X,Y] :
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] :
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(f2,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f2_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p39,plain,
( product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c16,c2]) ).
cnf(f3,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f3_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(p65,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p39,c3]) ).
cnf(f19,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f19_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(f20,axiom,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f20_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p43,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c19,c20]) ).
cnf(p198,plain,
( equalish(e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p65,p43]) ).
cnf(f18,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f18_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p42,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c18,c20]) ).
cnf(p798,plain,
( equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p198,p42]) ).
cnf(p40,plain,
( product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c16,c3]) ).
cnf(f1,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f1_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p69,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p40,c1]) ).
cnf(p237,plain,
( equalish(e_4,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p69,p42]) ).
cnf(f21,negated_conjecture,
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_1) ).
fof(f21_nnf,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( equalish(X0,X3)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p26,plain,
( equalish(X0,X2)
| ~ product(X2,X0,X1)
| ~ product(X2,X2,X2)
| ~ product(X0,X1,X2) ),
inference(factoring,[status(thm)],[c21]) ).
cnf(p934,plain,
( equalish(e_4,e_3)
| ~ product(e_3,e_4,e_2)
| ~ product(e_3,e_3,e_3)
| equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p237,p26]) ).
cnf(p955,plain,
( equalish(e_4,e_3)
| ~ product(e_3,e_4,e_2)
| equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p934,c20]) ).
cnf(p5071,plain,
( equalish(e_4,e_3)
| equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p798,p955]) ).
cnf(p5113,plain,
( equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p5071]) ).
cnf(p5119,plain,
( equalish(e_4,X0)
| ~ product(X0,e_2,e_2)
| equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5113,c19]) ).
cnf(p5316,plain,
( equalish(e_4,e_2)
| equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5119,c20]) ).
cnf(p5318,plain,
( equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p5316]) ).
cnf(p5327,plain,
( equalish(e_4,X0)
| ~ product(X0,e_2,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5318,c19]) ).
cnf(p5337,plain,
( ~ product(e_3,e_2,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p5327]) ).
cnf(p38,plain,
( product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(p60,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p38,c3]) ).
cnf(p141,plain,
( equalish(e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p60,p43]) ).
cnf(p31,plain,
( equalish(X2,X0)
| ~ product(X3,X0,X1)
| ~ product(X3,X2,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c20,c21]) ).
cnf(p554,plain,
( equalish(e_3,e_2)
| ~ product(X0,e_2,e_4)
| ~ product(X0,e_3,e_3)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p141,p31]) ).
cnf(p564,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_2,e_4)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p554,c20]) ).
cnf(p64,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p39,c1]) ).
cnf(p566,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p564,p64]) ).
cnf(p657,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p566,p42]) ).
cnf(p667,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(factoring,[status(thm)],[p657]) ).
cnf(p673,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p667,c19]) ).
cnf(p680,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p673,c20]) ).
cnf(p681,plain,
( product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(factoring,[status(thm)],[p680]) ).
cnf(p5343,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5337,p681]) ).
cnf(p5666,plain,
( equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p5343]) ).
cnf(p5674,plain,
( equalish(e_4,X0)
| ~ product(e_3,X0,e_1)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p5666,c18]) ).
cnf(p5733,plain,
( ~ product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p5674]) ).
cnf(p5737,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p5733,p681]) ).
cnf(p12685,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p5737]) ).
cnf(p12689,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p12685]) ).
cnf(p12691,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p12689]) ).
cnf(p12693,plain,
( equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p12691]) ).
cnf(p12699,plain,
( equalish(e_4,X0)
| ~ product(e_2,X0,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p12693,c18]) ).
cnf(p12716,plain,
( equalish(e_4,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p12699,c20]) ).
cnf(p12718,plain,
( equalish(e_3,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p12716]) ).
cnf(p5061,plain,
( equalish(e_3,e_2)
| ~ product(e_2,e_3,e_4)
| ~ product(e_2,e_2,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p798,p26]) ).
cnf(p5094,plain,
( equalish(e_3,e_2)
| ~ product(e_2,e_3,e_4)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5061,c20]) ).
cnf(p59,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p38,c2]) ).
cnf(p5095,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5094,p59]) ).
cnf(p5443,plain,
( equalish(e_3,X0)
| ~ product(X0,e_4,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p5095,c19]) ).
cnf(p6434,plain,
( ~ product(e_2,e_4,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p5443]) ).
cnf(p12759,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p12718,p6434]) ).
cnf(p13120,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p12759]) ).
cnf(p13123,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13120]) ).
cnf(p13126,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13123]) ).
cnf(p13133,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13126,p43]) ).
cnf(p13170,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13133]) ).
cnf(p13175,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13170,c18]) ).
cnf(p13250,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13175,c20]) ).
cnf(p13254,plain,
( product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13250]) ).
cnf(p12731,plain,
( equalish(e_4,X0)
| ~ product(e_2,X0,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p12718,c18]) ).
cnf(p12781,plain,
( ~ product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p12731]) ).
cnf(p13297,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13254,p12781]) ).
cnf(p13379,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13297]) ).
cnf(p13392,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13379]) ).
cnf(p13395,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13392]) ).
cnf(p13397,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13395]) ).
cnf(f15,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f15_nnf,plain,
~ equalish(e_4,e_3),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ equalish(e_4,e_3),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p13398,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p13397,c15]) ).
cnf(f14,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f14_nnf,plain,
~ equalish(e_4,e_2),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ equalish(e_4,e_2),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p13399,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p13398,c14]) ).
cnf(f12,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f12_nnf,plain,
~ equalish(e_3,e_4),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ equalish(e_3,e_4),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p13400,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[p13399,c12]) ).
cnf(f11,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f11_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p13401,plain,
$false,
inference(resolution,[status(thm)],[p13400,c11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n008.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 13:38:15 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 40.52/16.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.52/16.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------