%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 4.98s 6.10s
% Output : Proof 4.98s
% 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(f9,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(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c9,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)],[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(p24,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)],[c9,c1]) ).
cnf(f2,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f2_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p45,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)],[p24,c2]) ).
cnf(f19,negated_conjecture,
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
fof(f19_nnf,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p75,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)],[p45,c19]) ).
cnf(f13,axiom,
product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f13_nnf,plain,
! [X] : product1(X,X,X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : product1(X,X,X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p82,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)],[p75,c13]) ).
cnf(f16,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f16_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p84,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)],[p82,c16]) ).
cnf(f18,axiom,
product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f18_nnf,plain,
! [X] : product2(X,X,X),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X] : product2(X,X,X),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p89,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p84,c18]) ).
cnf(f11,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f11_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p29,plain,
( equalish(X0,X1)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[c11,c13]) ).
cnf(p95,plain,
( equalish(e_2,e_3)
| equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p89,p29]) ).
cnf(p100,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p95]) ).
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(p23,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)],[c9,c0]) ).
cnf(p39,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)],[p23,c2]) ).
cnf(p46,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)],[p39,c19]) ).
cnf(p51,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)],[p46,c13]) ).
cnf(p53,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)],[p51,c16]) ).
cnf(p57,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p53,c18]) ).
cnf(p58,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)],[p57,c19]) ).
cnf(p105,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)],[p100,p58]) ).
cnf(f15,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f15_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p31,plain,
( equalish(X0,X1)
| ~ product2(X0,X0,X1) ),
inference(resolution,[status(thm)],[c15,c18]) ).
cnf(p113,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)],[p105,p31]) ).
cnf(p116,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_1)
| equalish(e_2,e_3) ),
inference(factoring,[status(thm)],[p113]) ).
cnf(p121,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_3)
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[p116,p29]) ).
cnf(p125,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_3) ),
inference(factoring,[status(thm)],[p121]) ).
cnf(f6,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f6_nnf,plain,
~ equalish(e_2,e_3),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ equalish(e_2,e_3),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p126,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[p125,c6]) ).
cnf(f4,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f4_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p127,plain,
$false,
inference(resolution,[status(thm)],[p126,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n026.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Wed Sep 23 13:38:45 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.98/6.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.98/6.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------