%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 4.12s 1.29s
% Output : Proof 4.12s
% 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(f15,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(f15_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)],[f15]) ).
fof(f15_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)],[f15_nnf]) ).
cnf(c15,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)],[f15_sk]) ).
cnf(f7,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f7_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p30,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)],[c15,c7]) ).
cnf(f8,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f8_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p51,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)],[p30,c8]) ).
cnf(f25,negated_conjecture,
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
fof(f25_nnf,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,X,Y)
| ~ product1(Z1,Y,Z2)
| ~ product1(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p81,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)],[p51,c25]) ).
cnf(f19,axiom,
product1(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f19_nnf,plain,
! [X] : product1(X,X,X),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] : product1(X,X,X),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p88,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)],[p81,c19]) ).
cnf(f22,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f22_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p90,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)],[p88,c22]) ).
cnf(f24,axiom,
product2(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f24_nnf,plain,
! [X] : product2(X,X,X),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X] : product2(X,X,X),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p95,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p90,c24]) ).
cnf(f17,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f17_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p35,plain,
( equalish(X0,X1)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[c17,c19]) ).
cnf(p101,plain,
( equalish(e_2,e_3)
| equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p95,p35]) ).
cnf(p106,plain,
( equalish(e_2,e_3)
| product1(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p101]) ).
cnf(f6,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f6_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p29,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)],[c15,c6]) ).
cnf(p45,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)],[p29,c8]) ).
cnf(p52,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)],[p45,c25]) ).
cnf(p57,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)],[p52,c19]) ).
cnf(p59,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)],[p57,c22]) ).
cnf(p63,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p59,c24]) ).
cnf(p64,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)],[p63,c25]) ).
cnf(p111,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)],[p106,p64]) ).
cnf(f21,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f21_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p41,plain,
( equalish(X0,X1)
| ~ product2(X0,X0,X1) ),
inference(resolution,[status(thm)],[c21,c24]) ).
cnf(p119,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)],[p111,p41]) ).
cnf(p122,plain,
( equalish(e_1,e_3)
| product1(e_1,e_3,e_1)
| equalish(e_2,e_3) ),
inference(factoring,[status(thm)],[p119]) ).
cnf(p127,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_3)
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[p122,p35]) ).
cnf(p131,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_3) ),
inference(factoring,[status(thm)],[p127]) ).
cnf(f12,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f12_nnf,plain,
~ equalish(e_2,e_3),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ equalish(e_2,e_3),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p132,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[p131,c12]) ).
cnf(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f10_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p133,plain,
$false,
inference(resolution,[status(thm)],[p132,c10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.57 % Computer : n016.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 13:41:11 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.12/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.12/1.29 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------