%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 6.56s 6.49s
% Output : Proof 6.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 35 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 184 ( 83 ~; 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 : 96 ( 1 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,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(f25_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)],[f25]) ).
fof(f25_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)],[f25_nnf]) ).
cnf(c25,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)],[f25_sk]) ).
cnf(f17,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f17_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(p71,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)],[c25,c17]) ).
cnf(f18,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f18_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(p147,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)],[p71,c18]) ).
cnf(f28,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f28_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(f29,axiom,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f29_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p68,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c28,c29]) ).
cnf(p178,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p147,p68]) ).
cnf(f31,negated_conjecture,
( equalish(Y1,Y2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
fof(f31_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)],[f31]) ).
fof(f31_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)],[f31_nnf]) ).
cnf(c31,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)],[f31_sk]) ).
cnf(p36,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,X0) ),
inference(factoring,[status(thm)],[c31]) ).
cnf(p47,plain,
( equalish(X2,X1)
| ~ product(X2,X1,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c29,p36]) ).
cnf(p48,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(factoring,[status(thm)],[p47]) ).
cnf(p189,plain,
( equalish(e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p178,p48]) ).
cnf(f16,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f16_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(p70,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)],[c25,c16]) ).
cnf(p77,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)],[p70,c18]) ).
cnf(p110,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p77,p68]) ).
cnf(f30,negated_conjecture,
( equalish(X1,X2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_1) ).
fof(f30_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)],[f30]) ).
fof(f30_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)],[f30_nnf]) ).
cnf(c30,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)],[f30_sk]) ).
cnf(p32,plain,
( equalish(X0,X2)
| ~ product(X0,X3,X2)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,X0) ),
inference(factoring,[status(thm)],[c30]) ).
cnf(p44,plain,
( equalish(X2,X0)
| ~ product(X2,X1,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c29,p32]) ).
cnf(p120,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_3,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p110,p44]) ).
cnf(p203,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p189,p120]) ).
cnf(p214,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p203,p48]) ).
cnf(f24,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f24_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p219,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[p214,c24]) ).
cnf(f23,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f23_nnf,plain,
~ equalish(e_3,e_1),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
~ equalish(e_3,e_1),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p220,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[p219,c23]) ).
cnf(f22,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f22_nnf,plain,
~ equalish(e_2,e_3),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ equalish(e_2,e_3),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p221,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[p220,c22]) ).
cnf(f21,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f21_nnf,plain,
~ equalish(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ equalish(e_2,e_1),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p222,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[p221,c21]) ).
cnf(f20,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f20_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p223,plain,
$false,
inference(resolution,[status(thm)],[p222,c20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.38 % Computer : n015.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Wed Sep 23 13:39:00 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.56/6.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.56/6.49 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------