%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 4.30s 6.10s
% Output : Proof 4.30s
% 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(f25,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/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f25_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)],[f25]) ).
fof(f25_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)],[f25_nnf]) ).
cnf(c25,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)],[f25_sk]) ).
cnf(f17,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/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(p69,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)],[c25,c17]) ).
cnf(f18,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/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(p132,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)],[p69,c18]) ).
cnf(f35,negated_conjecture,
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
fof(f35_nnf,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p138,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)],[p132,c35]) ).
cnf(f29,axiom,
product1(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f29_nnf,plain,
! [X] : product1(X,X,X),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X] : product1(X,X,X),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p145,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)],[p138,c29]) ).
cnf(f32,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f32_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p147,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)],[p145,c32]) ).
cnf(f34,axiom,
product2(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f34_nnf,plain,
! [X] : product2(X,X,X),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X] : product2(X,X,X),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p152,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p147,c34]) ).
cnf(f27,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f27_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p66,plain,
( equalish(X0,X1)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[c27,c29]) ).
cnf(p158,plain,
( equalish(e_2,e_3)
| equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p152,p66]) ).
cnf(p163,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p158]) ).
cnf(f16,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/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(p68,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)],[c25,c16]) ).
cnf(p86,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)],[p68,c18]) ).
cnf(p93,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)],[p86,c35]) ).
cnf(p98,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)],[p93,c29]) ).
cnf(p100,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)],[p98,c32]) ).
cnf(p105,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p100,c34]) ).
cnf(p106,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)],[p105,c35]) ).
cnf(p168,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)],[p163,p106]) ).
cnf(f31,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f31_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p72,plain,
( equalish(X0,X1)
| ~ product2(X0,X0,X1) ),
inference(resolution,[status(thm)],[c31,c34]) ).
cnf(p176,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)],[p168,p72]) ).
cnf(p179,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_1)
| equalish(e_2,e_3) ),
inference(factoring,[status(thm)],[p176]) ).
cnf(p184,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_3)
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[p179,p66]) ).
cnf(p188,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_3) ),
inference(factoring,[status(thm)],[p184]) ).
cnf(f22,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/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(p189,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[p188,c22]) ).
cnf(f20,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/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(p190,plain,
$false,
inference(resolution,[status(thm)],[p189,c20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.36 % Computer : n011.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Wed Sep 23 13:37:03 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.30/6.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.30/6.10 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------