%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 73.58s 29.96s
% Output : Proof 73.58s
% 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(f26,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/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f26_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)],[f26]) ).
fof(f26_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)],[f26_nnf]) ).
cnf(c26,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)],[f26_sk]) ).
cnf(f12,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f12_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p50,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)],[c26,c12]) ).
cnf(f13,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f13_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p76,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)],[p50,c13]) ).
cnf(f29,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f29_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f30,axiom,
product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f30_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p55,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c29,c30]) ).
cnf(p221,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)],[p76,p55]) ).
cnf(f28,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f28_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p54,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c28,c30]) ).
cnf(p816,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)],[p221,p54]) ).
cnf(p51,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)],[c26,c13]) ).
cnf(f11,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f11_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(p80,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)],[p51,c11]) ).
cnf(p261,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)],[p80,p54]) ).
cnf(f31,negated_conjecture,
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
fof(f31_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)],[f31]) ).
fof(f31_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)],[f31_nnf]) ).
cnf(c31,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)],[f31_sk]) ).
cnf(p36,plain,
( equalish(X0,X2)
| ~ product(X2,X0,X1)
| ~ product(X2,X2,X2)
| ~ product(X0,X1,X2) ),
inference(factoring,[status(thm)],[c31]) ).
cnf(p938,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)],[p261,p36]) ).
cnf(p959,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)],[p938,c30]) ).
cnf(p4192,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)],[p816,p959]) ).
cnf(p4260,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)],[p4192]) ).
cnf(p4266,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)],[p4260,c29]) ).
cnf(p4331,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)],[p4266,c30]) ).
cnf(p4351,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)],[p4331]) ).
cnf(p4360,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)],[p4351,c29]) ).
cnf(p4376,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)],[p4360]) ).
cnf(p49,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)],[c26,c11]) ).
cnf(p71,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)],[p49,c13]) ).
cnf(p162,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)],[p71,p55]) ).
cnf(p41,plain,
( equalish(X2,X0)
| ~ product(X3,X0,X1)
| ~ product(X3,X2,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c30,c31]) ).
cnf(p583,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)],[p162,p41]) ).
cnf(p594,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)],[p583,c30]) ).
cnf(p75,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)],[p50,c11]) ).
cnf(p596,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)],[p594,p75]) ).
cnf(p678,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)],[p596,p54]) ).
cnf(p687,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)],[p678]) ).
cnf(p693,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)],[p687,c29]) ).
cnf(p700,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)],[p693,c30]) ).
cnf(p701,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)],[p700]) ).
cnf(p4382,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)],[p4376,p701]) ).
cnf(p4759,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)],[p4382]) ).
cnf(p4767,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)],[p4759,c28]) ).
cnf(p4836,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)],[p4767]) ).
cnf(p4839,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)],[p4836,p701]) ).
cnf(p26641,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)],[p4839]) ).
cnf(p26645,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)],[p26641]) ).
cnf(p26647,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)],[p26645]) ).
cnf(p26654,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)],[p26647]) ).
cnf(p26659,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)],[p26654,c28]) ).
cnf(p26718,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)],[p26659,c30]) ).
cnf(p26730,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)],[p26718]) ).
cnf(p4182,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)],[p816,p36]) ).
cnf(p4214,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)],[p4182,c30]) ).
cnf(p70,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)],[p49,c12]) ).
cnf(p4215,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)],[p4214,p70]) ).
cnf(p4548,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)],[p4215,c29]) ).
cnf(p5350,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)],[p4548]) ).
cnf(p26757,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)],[p26730,p5350]) ).
cnf(p27133,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)],[p26757]) ).
cnf(p27136,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)],[p27133]) ).
cnf(p27138,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)],[p27136]) ).
cnf(p27145,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)],[p27138,p55]) ).
cnf(p27219,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)],[p27145]) ).
cnf(p27224,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)],[p27219,c28]) ).
cnf(p27313,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)],[p27224,c30]) ).
cnf(p27314,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)],[p27313]) ).
cnf(p26739,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)],[p26730,c28]) ).
cnf(p26792,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)],[p26739]) ).
cnf(p27355,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)],[p27314,p26792]) ).
cnf(p27447,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)],[p27355]) ).
cnf(p27451,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)],[p27447]) ).
cnf(p27454,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)],[p27451]) ).
cnf(p27465,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)],[p27454]) ).
cnf(f25,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f25_nnf,plain,
~ equalish(e_4,e_3),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
~ equalish(e_4,e_3),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p27466,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p27465,c25]) ).
cnf(f24,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f24_nnf,plain,
~ equalish(e_4,e_2),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
~ equalish(e_4,e_2),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p27467,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p27466,c24]) ).
cnf(f22,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f22_nnf,plain,
~ equalish(e_3,e_4),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ equalish(e_3,e_4),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p27468,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[p27467,c22]) ).
cnf(f21,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f21_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p27472,plain,
$false,
inference(resolution,[status(thm)],[p27468,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n020.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 13:38:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 73.58/29.96 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 73.58/29.96 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------