%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP130-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 01:25:21 PM UTC 2026
% Result : Unsatisfiable 25.24s 22.39s
% Output : Proof 25.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 14
% Syntax : Number of formulae : 156 ( 29 unt; 0 def)
% Number of atoms : 548 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 495 ( 103 ~; 392 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 109 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( 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(f15_nnf,plain,
! [X,Y] :
( 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)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] :
( 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)],[f15_nnf]) ).
cnf(c15,plain,
( 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)],[f15_sk]) ).
cnf(f8,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f8_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p25,plain,
( 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)],[c15,c8]) ).
cnf(f6,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f6_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p60,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p25,c6]) ).
cnf(p23,plain,
( product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(p47,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p23,c8]) ).
cnf(f19,negated_conjecture,
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
fof(f19_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p20,plain,
( product(X1,X1,X0)
| ~ product(X0,X1,X1) ),
inference(factoring,[status(thm)],[c19]) ).
cnf(p114,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p47,p20]) ).
cnf(p119,plain,
( product(X0,e_3,e_3)
| ~ product(e_3,e_1,X0)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p114,c19]) ).
cnf(p154,plain,
( product(e_3,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p60,p119]) ).
cnf(f16,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f16_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p120,plain,
( equalish(e_1,X0)
| ~ product(e_3,e_3,X0)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p114,c16]) ).
cnf(p242,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p154,p120]) ).
cnf(p572,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p242]) ).
cnf(p701,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p572]) ).
cnf(p716,plain,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p701,p119]) ).
cnf(p3176,plain,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p716]) ).
cnf(p3295,plain,
( product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p3176]) ).
cnf(p22,plain,
( product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c15]) ).
cnf(p28,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,c6]) ).
cnf(f5,axiom,
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
fof(f5_nnf,plain,
! [X,Y,X1] :
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,X1] :
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p32,plain,
( ~ greater(e_3,X0)
| ~ next(e_1,X0)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p28,c5]) ).
cnf(f0,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f0_nnf,plain,
next(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
next(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p89,plain,
( ~ greater(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p32,c0]) ).
cnf(f4,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_2) ).
fof(f4_nnf,plain,
greater(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
greater(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p100,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p89,c4]) ).
cnf(f18,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f18_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p105,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p100,c18]) ).
cnf(p718,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p701,p105]) ).
cnf(p737,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p718]) ).
cnf(f17,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f17_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p743,plain,
( equalish(e_1,X0)
| ~ product(e_3,X0,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p737,c17]) ).
cnf(p754,plain,
( ~ product(e_3,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p743]) ).
cnf(p756,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p754,p114]) ).
cnf(p1076,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p756]) ).
cnf(p1078,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p1076]) ).
cnf(p104,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p100,c17]) ).
cnf(p1084,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p1078,p104]) ).
cnf(p1093,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p1084]) ).
cnf(p1094,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p1093]) ).
cnf(f7,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f7_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p46,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p23,c7]) ).
cnf(p106,plain,
( product(X0,e_2,e_1)
| ~ product(e_1,e_3,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p46,c19]) ).
cnf(p112,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p106]) ).
cnf(p1100,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1094,p112]) ).
cnf(p101,plain,
( product(X0,e_1,e_1)
| ~ product(e_1,e_2,X0)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p100,c19]) ).
cnf(p1109,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1100,p101]) ).
cnf(p1136,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p1109]) ).
cnf(p1140,plain,
( equalish(e_1,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1136,c17]) ).
cnf(p1146,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p1140]) ).
cnf(p1095,plain,
( product(X0,e_3,e_1)
| ~ product(e_1,e_1,X0)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1094,c19]) ).
cnf(p1103,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1095,p100]) ).
cnf(p1110,plain,
( product(e_2,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p1103]) ).
cnf(p1148,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1146,p1110]) ).
cnf(p1150,plain,
( equalish(e_1,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p1148]) ).
cnf(p1153,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p1150]) ).
cnf(p110,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p101]) ).
cnf(p1159,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1153,p110]) ).
cnf(p1160,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p1159]) ).
cnf(p1165,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1160,c18]) ).
cnf(p1179,plain,
( ~ product(e_3,e_1,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p1165]) ).
cnf(p3312,plain,
( equalish(e_1,e_3)
| product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p3295,p1179]) ).
cnf(p3317,plain,
( product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p3312]) ).
cnf(p117,plain,
( equalish(e_1,X0)
| ~ product(X0,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p47,c18]) ).
cnf(p3325,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p3317,p117]) ).
cnf(p3394,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p3325]) ).
cnf(p3396,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p3394]) ).
cnf(p3400,plain,
( equalish(e_1,X0)
| ~ product(X0,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p3396,c18]) ).
cnf(p3426,plain,
( ~ product(e_3,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p3400]) ).
cnf(p24,plain,
( 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)],[c15,c7]) ).
cnf(p56,plain,
( 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)],[p24,c8]) ).
cnf(p137,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p56,p20]) ).
cnf(p3442,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p3426,p137]) ).
cnf(p3427,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p3400]) ).
cnf(p3473,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p3442,p3427]) ).
cnf(p4600,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p3473]) ).
cnf(p4603,plain,
( equalish(e_1,e_2)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4600]) ).
cnf(p4605,plain,
( product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4603]) ).
cnf(p108,plain,
( equalish(e_2,X0)
| ~ product(e_1,X0,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p46,c17]) ).
cnf(p274,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p108,p47]) ).
cnf(p604,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p274,p106]) ).
cnf(p2383,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p604]) ).
cnf(p2395,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p2383]) ).
cnf(p2405,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p2395,c17]) ).
cnf(p2420,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p2405]) ).
cnf(p4619,plain,
( product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4605,p2420]) ).
cnf(p5721,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4619]) ).
cnf(p1164,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p1160,c17]) ).
cnf(p1178,plain,
( ~ product(e_1,e_3,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p1164]) ).
cnf(p5732,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5721,p1178]) ).
cnf(p5745,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5732]) ).
cnf(p5749,plain,
( equalish(e_2,X0)
| ~ product(e_1,X0,e_2)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5745,c17]) ).
cnf(p5791,plain,
( ~ product(e_1,e_3,e_2)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5749]) ).
cnf(p5798,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5791,p3396]) ).
cnf(p5843,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5798]) ).
cnf(p5845,plain,
( product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5843]) ).
cnf(p5856,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5845,p1178]) ).
cnf(p5860,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5856]) ).
cnf(p111,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_3,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p101,p46]) ).
cnf(p129,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p111,p20]) ).
cnf(p250,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p104,p129]) ).
cnf(p253,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p250]) ).
cnf(p259,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p253,p110]) ).
cnf(p260,plain,
( product(e_1,e_1,e_3)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p259]) ).
cnf(p262,plain,
( ~ greater(e_3,X0)
| ~ next(e_1,X0)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p260,c5]) ).
cnf(p267,plain,
( ~ greater(e_3,e_2)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p262,c0]) ).
cnf(p268,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p267,c4]) ).
cnf(p272,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p268,c17]) ).
cnf(p279,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p272]) ).
cnf(p5867,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_3)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5860,p279]) ).
cnf(p5879,plain,
( equalish(e_2,e_3)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5867]) ).
cnf(f12,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f12_nnf,plain,
~ equalish(e_2,e_3),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ equalish(e_2,e_3),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p5889,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5879,c12]) ).
cnf(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f10_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p5890,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p5889,c10]) ).
cnf(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f9_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p5891,plain,
$false,
inference(resolution,[status(thm)],[p5890,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.41 % CPULimit : 300
% 0.07/15.41 % WCLimit : 300
% 0.07/15.41 % DateTime : Wed Sep 23 13:47:01 UTC 2026
% 0.07/15.41 % CPUTime :
% 0.07/15.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.24/22.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.24/22.39 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------