%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP133-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:25:23 PM UTC 2026
% Result : Unsatisfiable 15.97s 7.78s
% Output : Proof 15.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 16
% Syntax : Number of formulae : 180 ( 37 unt; 0 def)
% Number of atoms : 675 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 614 ( 119 ~; 495 |; 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 : 118 ( 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/sandbox/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/sandbox/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/sandbox/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(p59,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(f19,negated_conjecture,
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f19_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p222,plain,
( product(e_3,X0,e_3)
| ~ product(e_1,e_3,X0)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p59,c19]) ).
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(p44,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(p231,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_3,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p222,p44]) ).
cnf(f17,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/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(p241,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,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)],[p231,c17]) ).
cnf(p421,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| equalish(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)],[p241,p59]) ).
cnf(p575,plain,
( product(e_3,e_1,e_2)
| equalish(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(factoring,[status(thm)],[p421]) ).
cnf(p577,plain,
( equalish(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(factoring,[status(thm)],[p575]) ).
cnf(p594,plain,
( product(e_2,X0,e_3)
| ~ product(e_1,e_3,X0)
| equalish(e_3,e_1)
| 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)],[p577,c19]) ).
cnf(p620,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_3)
| equalish(e_3,e_1)
| 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)],[p594,p44]) ).
cnf(p2107,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_3)
| equalish(e_3,e_1)
| 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)],[p620]) ).
cnf(p2243,plain,
( product(e_2,e_3,e_3)
| equalish(e_3,e_1)
| 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)],[p2107]) ).
cnf(f18,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/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(p2248,plain,
( equalish(e_3,X0)
| ~ product(X0,e_1,e_1)
| product(e_2,e_3,e_3)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p2243,c18]) ).
cnf(p2288,plain,
( ~ product(e_1,e_1,e_1)
| product(e_2,e_3,e_3)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p2248]) ).
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(p30,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p22,c8]) ).
cnf(p85,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p30,c18]) ).
cnf(p358,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p85,p44]) ).
cnf(p20,plain,
( product(X1,X1,X0)
| ~ product(X0,X0,X1) ),
inference(factoring,[status(thm)],[c19]) ).
cnf(p768,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p358,p20]) ).
cnf(p823,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p768,p20]) ).
cnf(f16,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/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(p868,plain,
( equalish(e_3,X0)
| ~ product(e_2,e_2,X0)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p823,c16]) ).
cnf(p1123,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p868]) ).
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/sandbox/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(p33,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/sandbox/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(p92,plain,
( ~ greater(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p33,c0]) ).
cnf(f4,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/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(p371,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p92,c4]) ).
cnf(p797,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p371,p20]) ).
cnf(p1135,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p1123,p797]) ).
cnf(p1138,plain,
( equalish(e_3,X0)
| ~ product(e_1,X0,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p1135,c17]) ).
cnf(p1210,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p1138]) ).
cnf(p1212,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p1210,p371]) ).
cnf(p1213,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p1212]) ).
cnf(p1214,plain,
( product(e_1,X0,e_1)
| ~ product(e_3,e_1,X0)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p1213,c19]) ).
cnf(p1220,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p1214]) ).
cnf(p84,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p30,c17]) ).
cnf(p349,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| equalish(e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p84,p59]) ).
cnf(p722,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| equalish(e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p349,p20]) ).
cnf(p728,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p722,p20]) ).
cnf(p737,plain,
( equalish(e_3,X0)
| ~ product(X0,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p728,c18]) ).
cnf(p990,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p737]) ).
cnf(p995,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p990,p371]) ).
cnf(p1223,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p1220,p995]) ).
cnf(p2063,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p1223]) ).
cnf(p2066,plain,
( product(e_2,e_2,e_3)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2063]) ).
cnf(p2067,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2066]) ).
cnf(p2070,plain,
( equalish(e_3,X0)
| ~ product(e_2,e_2,X0)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2067,c16]) ).
cnf(p2085,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2070]) ).
cnf(p2089,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2085,p797]) ).
cnf(p2090,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2089]) ).
cnf(p2093,plain,
( ~ greater(e_3,X0)
| ~ next(e_1,X0)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2090,c5]) ).
cnf(p2109,plain,
( ~ greater(e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2093,c0]) ).
cnf(p2110,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2109,c4]) ).
cnf(p2292,plain,
( equalish(e_3,e_1)
| product(e_2,e_3,e_3)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p2288,p2110]) ).
cnf(p2299,plain,
( product(e_2,e_3,e_3)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p2292]) ).
cnf(p149,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)],[p44,c18]) ).
cnf(p2305,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p2299,p149]) ).
cnf(p2336,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p2305]) ).
cnf(p2338,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p2336]) ).
cnf(p2342,plain,
( equalish(e_1,X0)
| ~ product(X0,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p2338,c18]) ).
cnf(p2358,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p2342]) ).
cnf(f7,axiom,
group_element(e_2),
file('/export/starexec/sandbox/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(p43,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(p135,plain,
( equalish(e_1,X0)
| ~ product(X0,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p43,c18]) ).
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(p53,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p24,c6]) ).
cnf(p183,plain,
( product(e_3,X0,e_2)
| ~ product(e_1,e_2,X0)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p53,c19]) ).
cnf(p193,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_3,e_3,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p183,p43]) ).
cnf(p201,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p193,p20]) ).
cnf(p405,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p135,p201]) ).
cnf(p539,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p405]) ).
cnf(p541,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p539]) ).
cnf(p542,plain,
( product(e_2,X0,e_2)
| ~ product(e_1,e_2,X0)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p541,c19]) ).
cnf(p550,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p542,p43]) ).
cnf(p1576,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p550]) ).
cnf(p1597,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p1576]) ).
cnf(p2382,plain,
( product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p2358,p1597]) ).
cnf(p2713,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p2382]) ).
cnf(p2115,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2110,c18]) ).
cnf(p2721,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p2713,p2115]) ).
cnf(p2800,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p2721]) ).
cnf(p2812,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p2800]) ).
cnf(p2815,plain,
( equalish(e_3,X0)
| ~ product(e_1,X0,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2812,c17]) ).
cnf(p2872,plain,
( ~ product(e_1,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2815]) ).
cnf(p2884,plain,
( equalish(e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2872,p2110]) ).
cnf(p2903,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2884]) ).
cnf(p2341,plain,
( equalish(e_3,X0)
| ~ product(e_1,X0,e_2)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p2338,c17]) ).
cnf(p2914,plain,
( equalish(e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2903,p2341]) ).
cnf(p2951,plain,
( equalish(e_3,e_2)
| equalish(e_1,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2914]) ).
cnf(p2954,plain,
( equalish(e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2951]) ).
cnf(p2114,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2110,c17]) ).
cnf(p2968,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2954,p2114]) ).
cnf(p2978,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2968]) ).
cnf(p219,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p201,c17]) ).
cnf(p402,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p219,p53]) ).
cnf(p503,plain,
( product(e_2,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p402]) ).
cnf(p506,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p503]) ).
cnf(p511,plain,
( equalish(e_2,X0)
| ~ product(X0,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p506,c18]) ).
cnf(p516,plain,
( ~ product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p511]) ).
cnf(p805,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p371,p516]) ).
cnf(p810,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p797,c17]) ).
cnf(p853,plain,
( equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| 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)],[p805,p810]) ).
cnf(p1058,plain,
( equalish(e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p853]) ).
cnf(p1060,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1058]) ).
cnf(p1069,plain,
( equalish(e_2,X0)
| ~ product(e_1,X0,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1060,c17]) ).
cnf(p1075,plain,
( ~ product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1069]) ).
cnf(p1077,plain,
( product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1075,p371]) ).
cnf(p1082,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1077]) ).
cnf(p811,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p797,c18]) ).
cnf(p1088,plain,
( equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1082,p811]) ).
cnf(p1096,plain,
( equalish(e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1088]) ).
cnf(p1098,plain,
( equalish(e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1096]) ).
cnf(p1103,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[p1098,c17]) ).
cnf(p2984,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2978,p1103]) ).
cnf(p2987,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p2984]) ).
cnf(f14,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f14_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p2988,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p2987,c14]) ).
cnf(f13,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f13_nnf,plain,
~ equalish(e_3,e_1),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ equalish(e_3,e_1),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p2989,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p2988,c13]) ).
cnf(f11,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f11_nnf,plain,
~ equalish(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ equalish(e_2,e_1),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p2994,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p2989,c11]) ).
cnf(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/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(p2995,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p2994,c10]) ).
cnf(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/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(p2996,plain,
$false,
inference(resolution,[status(thm)],[p2995,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP133-2.003 : 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 : n011.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 13:48:33 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.97/7.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.97/7.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------