%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:25:18 PM UTC 2026
% Result : Unsatisfiable 4.09s 1.53s
% Output : Proof 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 27 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 145 ( 58 ~; 87 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f4_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(f0,axiom,
( product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f0_nnf,plain,
! [X,Y] :
( product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p23,plain,
( product(e_3,e_1,X0)
| product(e_2,e_1,X0)
| product(e_1,e_1,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(f6,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f6_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p43,plain,
( product(e_3,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p23,c6]) ).
cnf(f3,negated_conjecture,
( ~ product(X,Y,Z1)
| ~ product(Z1,Z2,X)
| product(Y,X,Z2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
fof(f3_nnf,plain,
! [Y,X,Z2,Z1] :
( ~ product(X,Y,Z1)
| ~ product(Z1,Z2,X)
| product(Y,X,Z2) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Y,X,Z2,Z1] :
( ~ product(X,Y,Z1)
| ~ product(Z1,Z2,X)
| product(Y,X,Z2) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ product(X1,X0,X3)
| ~ product(X3,X2,X1)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p53,plain,
( ~ product(e_3,X0,e_3)
| product(X0,e_3,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p43,c3]) ).
cnf(f17,axiom,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f17_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p79,plain,
( product(e_3,e_3,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p53,c17]) ).
cnf(f18,negated_conjecture,
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f18_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p22,plain,
( product(X1,X1,X0)
| ~ product(X0,X0,X1) ),
inference(factoring,[status(thm)],[c18]) ).
cnf(p83,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p79,p22]) ).
cnf(p87,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(factoring,[status(thm)],[p83]) ).
cnf(f5,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f5_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(p42,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[p23,c5]) ).
cnf(p45,plain,
( ~ product(e_2,X0,e_3)
| product(X0,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[p42,c3]) ).
cnf(p94,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p87,p45]) ).
cnf(f15,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f15_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p40,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c15,c17]) ).
cnf(p107,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p94,p40]) ).
cnf(p117,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p107,p40]) ).
cnf(f14,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f14_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p38,plain,
( equalish(X0,X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c14,c17]) ).
cnf(p127,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[p117,p38]) ).
cnf(p136,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| equalish(e_1,e_2)
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[p127,p38]) ).
cnf(p138,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_2)
| equalish(e_2,e_1) ),
inference(factoring,[status(thm)],[p136]) ).
cnf(f9,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f9_nnf,plain,
~ equalish(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ equalish(e_2,e_1),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p139,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p138,c9]) ).
cnf(f8,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f8_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p142,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p139,c8]) ).
cnf(f7,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f7_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p143,plain,
$false,
inference(resolution,[status(thm)],[p142,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.78 % Computer : n004.cluster.edu
% 0.09/0.78 % Model : x86_64 x86_64
% 0.09/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.78 % Memory : 8046.5625MB
% 0.09/0.78 % OS : Linux 6.8.0-71-generic
% 0.09/0.78 % CPULimit : 300
% 0.09/0.78 % WCLimit : 300
% 0.09/0.78 % DateTime : Wed Sep 23 13:40:51 UTC 2026
% 0.09/0.79 % CPUTime :
% 0.09/0.79 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.09/1.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.09/1.53 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------