%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP124-8.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:25:17 PM UTC 2026
% Result : Unsatisfiable 24.24s 4.03s
% Output : Proof 24.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 14
% Syntax : Number of formulae : 124 ( 31 unt; 0 def)
% Number of atoms : 470 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 429 ( 83 ~; 346 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 119 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f37,axiom,
( product1(X,Y,e_4)
| product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f37_nnf,plain,
! [X,Y] :
( product1(X,Y,e_4)
| product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [X,Y] :
( product1(X,Y,e_4)
| product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
( product1(X0,X1,e_4)
| product1(X0,X1,e_3)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(f24,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f24_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(p72,plain,
( product1(e_4,X0,e_4)
| product1(e_4,X0,e_3)
| product1(e_4,X0,e_2)
| product1(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c37,c24]) ).
cnf(f22,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f22_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(p162,plain,
( product1(e_4,e_2,e_4)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p72,c22]) ).
cnf(f39,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f39_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(f41,axiom,
product1(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f41_nnf,plain,
! [X] : product1(X,X,X),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [X] : product1(X,X,X),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c41,plain,
product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p73,plain,
( equalish(X0,X1)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[c39,c41]) ).
cnf(p540,plain,
( equalish(e_4,e_2)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p162,p73]) ).
cnf(f47,negated_conjecture,
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2a) ).
fof(f47_nnf,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c47,plain,
( product2(X3,X1,X0)
| ~ product1(X2,X0,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p1611,plain,
( product2(X0,e_2,e_4)
| ~ product1(e_3,e_4,X0)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p540,c47]) ).
cnf(f23,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f23_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(p71,plain,
( product1(e_3,X0,e_4)
| product1(e_3,X0,e_3)
| product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c37,c23]) ).
cnf(p152,plain,
( product1(e_3,e_4,e_4)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p71,c24]) ).
cnf(f40,axiom,
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f40_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p74,plain,
( equalish(X1,X0)
| ~ product1(X0,X1,X1) ),
inference(resolution,[status(thm)],[c40,c41]) ).
cnf(p481,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p152,p74]) ).
cnf(p1290,plain,
( product2(X0,e_4,e_3)
| ~ product1(e_3,e_3,X0)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p481,c47]) ).
cnf(p1301,plain,
( product2(e_3,e_4,e_3)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1290,c41]) ).
cnf(f44,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f44_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p1303,plain,
( equalish(e_4,X0)
| ~ product2(e_3,X0,e_3)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1301,c44]) ).
cnf(f46,axiom,
product2(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f46_nnf,plain,
! [X] : product2(X,X,X),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [X] : product2(X,X,X),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p1306,plain,
( equalish(e_4,e_3)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1303,c46]) ).
cnf(p1317,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p1306]) ).
cnf(p1621,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| product2(e_2,e_2,e_4)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1611,p1317]) ).
cnf(f43,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f43_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p1628,plain,
( equalish(e_4,X0)
| ~ product2(e_2,e_2,X0)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1621,c43]) ).
cnf(p1662,plain,
( equalish(e_4,e_2)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1628,c46]) ).
cnf(p1663,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(factoring,[status(thm)],[p1662]) ).
cnf(p1667,plain,
( equalish(e_4,X0)
| ~ product1(X0,e_2,e_2)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1663,c40]) ).
cnf(p1683,plain,
( equalish(e_4,e_2)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1667,c41]) ).
cnf(p1684,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_1) ),
inference(factoring,[status(thm)],[p1683]) ).
cnf(p1694,plain,
( equalish(e_4,X0)
| ~ product1(X0,e_2,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1684,c40]) ).
cnf(p1703,plain,
( ~ product1(e_3,e_2,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p1694]) ).
cnf(p151,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p71,c22]) ).
cnf(p70,plain,
( product1(e_2,X0,e_4)
| product1(e_2,X0,e_3)
| product1(e_2,X0,e_2)
| product1(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c37,c22]) ).
cnf(p140,plain,
( product1(e_2,e_4,e_4)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p70,c24]) ).
cnf(p168,plain,
( equalish(e_4,e_2)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p140,p74]) ).
cnf(p169,plain,
( product2(X0,e_4,e_2)
| ~ product1(e_3,e_2,X0)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p168,c47]) ).
cnf(p276,plain,
( product2(e_4,e_4,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p151,p169]) ).
cnf(p80,plain,
( equalish(X0,X1)
| ~ product2(X0,X0,X1) ),
inference(resolution,[status(thm)],[c43,c46]) ).
cnf(p278,plain,
( equalish(e_4,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p276,p80]) ).
cnf(p281,plain,
( equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p278]) ).
cnf(p285,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p281,p73]) ).
cnf(p292,plain,
( equalish(e_3,X0)
| ~ product1(X0,e_2,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p285,c40]) ).
cnf(p307,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p292,c41]) ).
cnf(p310,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p307]) ).
cnf(p1706,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1703,p310]) ).
cnf(p1714,plain,
( equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p1706]) ).
cnf(p1717,plain,
( equalish(e_4,X0)
| ~ product1(e_3,X0,e_1)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1714,c39]) ).
cnf(p1763,plain,
( ~ product1(e_3,e_2,e_1)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p1717]) ).
cnf(p1776,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1763,p310]) ).
cnf(p7330,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p1776]) ).
cnf(p7336,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7330]) ).
cnf(p7338,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7336]) ).
cnf(p7340,plain,
( equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7338]) ).
cnf(p7343,plain,
( equalish(e_4,X0)
| ~ product1(e_2,X0,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7340,c39]) ).
cnf(p7448,plain,
( equalish(e_4,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7343,c41]) ).
cnf(p7449,plain,
( equalish(e_3,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7448]) ).
cnf(p1318,plain,
( product2(X0,e_4,e_3)
| ~ product1(e_2,e_3,X0)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1317,c47]) ).
cnf(p139,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p70,c23]) ).
cnf(p1338,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| product2(e_4,e_4,e_3)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1318,p139]) ).
cnf(p1410,plain,
( equalish(e_4,e_3)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1338,p80]) ).
cnf(p1419,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p1410]) ).
cnf(p1423,plain,
( equalish(e_3,X0)
| ~ product1(X0,e_4,e_1)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p1419,c40]) ).
cnf(p7455,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_4,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7449,p1423]) ).
cnf(p7606,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7455]) ).
cnf(p7608,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7606]) ).
cnf(p7613,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7608,p74]) ).
cnf(p7619,plain,
( product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7613]) ).
cnf(p7632,plain,
( equalish(e_3,X0)
| ~ product1(e_2,X0,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7619,c39]) ).
cnf(p7690,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7632,c41]) ).
cnf(p7692,plain,
( product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7690]) ).
cnf(p7452,plain,
( equalish(e_4,X0)
| ~ product1(e_2,X0,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7449,c39]) ).
cnf(p7490,plain,
( ~ product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7452]) ).
cnf(p7715,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7692,p7490]) ).
cnf(p7741,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7715]) ).
cnf(p7744,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7741]) ).
cnf(p7747,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7744]) ).
cnf(f36,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f36_nnf,plain,
~ equalish(e_4,e_3),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
~ equalish(e_4,e_3),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p7748,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7747,c36]) ).
cnf(f35,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f35_nnf,plain,
~ equalish(e_4,e_2),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
~ equalish(e_4,e_2),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p7749,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[p7748,c35]) ).
cnf(f32,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f32_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p7750,plain,
$false,
inference(resolution,[status(thm)],[p7749,c32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-8.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 13:41:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.24/4.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.24/4.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------