%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 01:25:15 PM UTC 2026
% Result : Unsatisfiable 5.17s 1.22s
% Output : Proof 5.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 27 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 154 ( 57 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 91 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f11,axiom,
( product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f11_nnf,plain,
! [X,Y] :
( product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y] :
( product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( product1(X0,X1,e_3)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(f3,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(p34,plain,
( product1(e_2,X0,e_3)
| product1(e_2,X0,e_2)
| product1(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c11,c3]) ).
cnf(f4,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f4_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p79,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p34,c4]) ).
cnf(f21,negated_conjecture,
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
fof(f21_nnf,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p101,plain,
( product2(X0,e_2,e_3)
| ~ product1(e_3,e_3,X0)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p79,c21]) ).
cnf(f15,axiom,
product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f15_nnf,plain,
! [X] : product1(X,X,X),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X] : product1(X,X,X),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p108,plain,
( product2(e_3,e_2,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p101,c15]) ).
cnf(f18,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f18_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p112,plain,
( equalish(e_2,X0)
| ~ product2(e_3,X0,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p108,c18]) ).
cnf(f20,axiom,
product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f20_nnf,plain,
! [X] : product2(X,X,X),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X] : product2(X,X,X),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p115,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p112,c20]) ).
cnf(f13,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f13_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p39,plain,
( equalish(X0,X1)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[c13,c15]) ).
cnf(p121,plain,
( equalish(e_2,e_3)
| equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p115,p39]) ).
cnf(p128,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p121]) ).
cnf(f2,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p33,plain,
( product1(e_1,X0,e_3)
| product1(e_1,X0,e_2)
| product1(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(p67,plain,
( product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p33,c4]) ).
cnf(p72,plain,
( product2(X0,e_1,e_3)
| ~ product1(e_3,e_3,X0)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p67,c21]) ).
cnf(p77,plain,
( product2(e_3,e_1,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p72,c15]) ).
cnf(p81,plain,
( equalish(e_1,X0)
| ~ product2(e_3,X0,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p77,c18]) ).
cnf(p83,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p81,c20]) ).
cnf(p84,plain,
( product2(X0,e_1,e_3)
| ~ product1(e_2,e_3,X0)
| equalish(e_1,e_3)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p83,c21]) ).
cnf(p133,plain,
( product2(e_1,e_1,e_3)
| equalish(e_1,e_3)
| product1(e_1,e_3,e_1)
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[p128,p84]) ).
cnf(f17,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f17_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p45,plain,
( equalish(X0,X1)
| ~ product2(X0,X0,X1) ),
inference(resolution,[status(thm)],[c17,c20]) ).
cnf(p140,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_3)
| product1(e_1,e_3,e_1)
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[p133,p45]) ).
cnf(p144,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_1)
| equalish(e_2,e_3) ),
inference(factoring,[status(thm)],[p140]) ).
cnf(p149,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_3)
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[p144,p39]) ).
cnf(p153,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_3) ),
inference(factoring,[status(thm)],[p149]) ).
cnf(f8,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f8_nnf,plain,
~ equalish(e_2,e_3),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ equalish(e_2,e_3),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p154,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[p153,c8]) ).
cnf(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f6_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p155,plain,
$false,
inference(resolution,[status(thm)],[p154,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Sep 23 13:37:48 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.17/1.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.17/1.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------