%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP125-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 5.29s 1.20s
% Output : Proof 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 24 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 151 ( 58 ~; 93 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 85 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,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(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c9,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)],[f9_sk]) ).
cnf(f1,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f1_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p21,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)],[c9,c1]) ).
cnf(f0,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f0_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p28,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)],[p21,c0]) ).
cnf(p20,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)],[c9,c0]) ).
cnf(p26,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)],[p20,c1]) ).
cnf(f14,negated_conjecture,
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f14_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p30,plain,
( product(e_3,X0,e_1)
| ~ product(e_2,e_1,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p26,c14]) ).
cnf(p49,plain,
( product(e_3,e_3,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)],[p28,p30]) ).
cnf(f10,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f10_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f13,axiom,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f13_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p18,plain,
( equalish(X0,X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c10,c13]) ).
cnf(p60,plain,
( equalish(e_3,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)],[p49,p18]) ).
cnf(f11,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f11_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p24,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c11,c13]) ).
cnf(p67,plain,
( equalish(e_2,e_1)
| equalish(e_3,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)],[p60,p24]) ).
cnf(f12,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f12_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p25,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c12,c13]) ).
cnf(p73,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p67,p25]) ).
cnf(p79,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p73,p25]) ).
cnf(p81,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p79]) ).
cnf(p86,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p81,p24]) ).
cnf(p88,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p86]) ).
cnf(f7,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f7_nnf,plain,
~ equalish(e_3,e_1),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ equalish(e_3,e_1),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p90,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[p88,c7]) ).
cnf(f5,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f5_nnf,plain,
~ equalish(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ equalish(e_2,e_1),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p91,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p90,c5]) ).
cnf(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f3_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p92,plain,
$false,
inference(resolution,[status(thm)],[p91,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP125-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 13:42:33 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.29/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.29/1.20 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------