%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP123-2.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 01:25:14 PM UTC 2026
% Result : Unsatisfiable 4.18s 1.26s
% Output : Proof 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 31 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 181 ( 80 ~; 101 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 97 ( 1 sgn 38 !; 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(p32,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(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(p59,plain,
( 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)],[p32,c7]) ).
cnf(f19,axiom,
product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f19_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(f21,negated_conjecture,
( equalish(Y1,Y2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_2) ).
fof(f21_nnf,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(Y1,Y2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(Y1,Y2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( equalish(X1,X4)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p26,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,X0) ),
inference(factoring,[status(thm)],[c21]) ).
cnf(p37,plain,
( equalish(X2,X1)
| ~ product(X2,X1,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c19,p26]) ).
cnf(p39,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(factoring,[status(thm)],[p37]) ).
cnf(p146,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p59,p39]) ).
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(p156,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_2)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p146,c18]) ).
cnf(p183,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p156,c19]) ).
cnf(p187,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p183]) ).
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(p30,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(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)],[p30,c7]) ).
cnf(f20,negated_conjecture,
( equalish(X1,X2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_1) ).
fof(f20_nnf,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( equalish(X0,X3)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p22,plain,
( equalish(X0,X2)
| ~ product(X0,X3,X2)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,X0) ),
inference(factoring,[status(thm)],[c20]) ).
cnf(p34,plain,
( equalish(X2,X0)
| ~ product(X2,X1,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c19,p22]) ).
cnf(p48,plain,
( equalish(e_3,e_1)
| ~ product(e_3,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p43,p34]) ).
cnf(p198,plain,
( equalish(e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p187,p48]) ).
cnf(p42,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c18,c19]) ).
cnf(p212,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p198,p42]) ).
cnf(p218,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p212,p39]) ).
cnf(f14,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/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(p222,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p218,c14]) ).
cnf(f13,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/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(p223,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[p222,c13]) ).
cnf(f11,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/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(p234,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p223,c11]) ).
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(p235,plain,
$false,
inference(resolution,[status(thm)],[p234,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 13:40:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.18/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/1.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------