%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 01:25:22 PM UTC 2026
% Result : Unsatisfiable 0.13s 1.01s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 13 unt; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 204 ( 77 ~; 127 |; 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 : 116 ( 1 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,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/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f13_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)],[f13]) ).
fof(f13_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)],[f13_nnf]) ).
cnf(c13,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)],[f13_sk]) ).
cnf(f6,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/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(p33,plain,
( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c13,c6]) ).
cnf(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/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(p128,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p33,c4]) ).
cnf(f2,negated_conjecture,
( ~ product(X,Z1,Z2)
| ~ product(Z2,Y,X)
| product(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_1) ).
fof(f2_nnf,plain,
! [X,Y,Z1,Z2] :
( ~ product(X,Z1,Z2)
| ~ product(Z2,Y,X)
| product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z1,Z2] :
( ~ product(X,Z1,Z2)
| ~ product(Z2,Y,X)
| product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ product(X0,X2,X3)
| ~ product(X3,X1,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p18,plain,
( ~ product(X0,X1,X0)
| product(X0,X1,X1) ),
inference(factoring,[status(thm)],[c2]) ).
cnf(p525,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p128,p18]) ).
cnf(p671,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p525]) ).
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/sandbox2/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(p22,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(p61,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)],[p22,c6]) ).
cnf(p186,plain,
( product(e_3,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p61,p18]) ).
cnf(f17,negated_conjecture,
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
fof(f17_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p21,plain,
( product(X1,X1,X0)
| ~ product(X0,X1,X1) ),
inference(factoring,[status(thm)],[c17]) ).
cnf(p215,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)],[p186,p21]) ).
cnf(p300,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(factoring,[status(thm)],[p215]) ).
cnf(p301,plain,
( ~ product(e_3,X0,e_2)
| product(e_3,e_1,X0)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p300,c2]) ).
cnf(p678,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p671,p301]) ).
cnf(p782,plain,
( product(e_1,e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p678]) ).
cnf(f1,axiom,
( product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
fof(f1_nnf,plain,
! [X,Y] :
( product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p24,plain,
( product(X0,e_3,X0)
| product(X0,e_2,X0)
| product(X0,e_1,X0)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c1]) ).
cnf(p81,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p24,c4]) ).
cnf(f3,negated_conjecture,
( ~ product(X,Y,Z1)
| ~ product(Z2,Y,X)
| product(X,Z1,Z2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_2) ).
fof(f3_nnf,plain,
! [X,Z1,Z2,Y] :
( ~ product(X,Y,Z1)
| ~ product(Z2,Y,X)
| product(X,Z1,Z2) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Z1,Z2,Y] :
( ~ product(X,Y,Z1)
| ~ product(Z2,Y,X)
| product(X,Z1,Z2) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ product(X0,X3,X1)
| ~ product(X2,X3,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p19,plain,
( ~ product(X0,X1,X0)
| product(X0,X0,X0) ),
inference(factoring,[status(thm)],[c3]) ).
cnf(p249,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p81,p19]) ).
cnf(p423,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p249]) ).
cnf(p426,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p423,p19]) ).
cnf(p437,plain,
product(e_1,e_1,e_1),
inference(factoring,[status(thm)],[p426]) ).
cnf(f16,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f16_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p449,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[p437,c16]) ).
cnf(p790,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[p782,p449]) ).
cnf(f14,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/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(p447,plain,
( equalish(e_1,X0)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[p437,c14]) ).
cnf(p798,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p790,p447]) ).
cnf(p801,plain,
equalish(e_1,e_3),
inference(factoring,[status(thm)],[p798]) ).
cnf(f8,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/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(p808,plain,
$false,
inference(resolution,[status(thm)],[p801,c8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.57 % Computer : n018.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Wed Sep 23 13:49:05 UTC 2026
% 0.13/0.57 % CPUTime :
% 0.13/0.57 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/1.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/1.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------