%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:25:22 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.83s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 16 unt; 0 def)
% Number of atoms : 206 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 210 ( 73 ~; 137 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 84 ( 3 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f7_nnf,plain,
! [X,Y] :
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f4_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p24,plain,
( product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f3_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(p48,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p24,c3]) ).
cnf(f10,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f10_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p22,plain,
( product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c7]) ).
cnf(p25,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,c3]) ).
cnf(p37,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,X0)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[c10,p25]) ).
cnf(p85,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p48,p37]) ).
cnf(p26,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p22,c4]) ).
cnf(f11,negated_conjecture,
( equalish(X1,X2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_1) ).
fof(f11_nnf,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,Y2,X2)
| ~ product(Z2,Y1,X1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( equalish(X0,X3)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p14,plain,
( equalish(X0,X2)
| ~ product(X2,X1,X0)
| ~ product(X2,X3,X2)
| ~ product(X0,X1,X2) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(p28,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_1,e_1)
| ~ product(e_2,X0,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p25,p14]) ).
cnf(p59,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p26,p28]) ).
cnf(p111,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p85,p59]) ).
cnf(p128,plain,
( equalish(e_1,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p111]) ).
cnf(p138,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p128]) ).
cnf(f9,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f9_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p142,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p138,c9]) ).
cnf(p154,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p142,p85]) ).
cnf(p157,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p154]) ).
cnf(p158,plain,
( equalish(e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p157]) ).
cnf(p13,plain,
( equalish(X0,X2)
| ~ product(X0,X3,X2)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,X0) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(p168,plain,
( equalish(e_1,X0)
| ~ product(e_1,X1,X0)
| ~ product(X0,X1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p158,p13]) ).
cnf(p179,plain,
( ~ product(e_1,X0,e_2)
| ~ product(e_2,X0,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p168]) ).
cnf(p58,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p26,c9]) ).
cnf(p88,plain,
( product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p58,p48]) ).
cnf(p183,plain,
( product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| ~ product(e_1,e_2,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p179,p88]) ).
cnf(p189,plain,
( product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p183]) ).
cnf(p23,plain,
( product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(p47,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p23,c4]) ).
cnf(p190,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p189,p47]) ).
cnf(p174,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p158,c10]) ).
cnf(p178,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p174]) ).
cnf(p198,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p190,p178]) ).
cnf(p206,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p198]) ).
cnf(p208,plain,
( product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p206]) ).
cnf(p173,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p158,c9]) ).
cnf(p177,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p173]) ).
cnf(p216,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p208,p177]) ).
cnf(p226,plain,
( equalish(e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p216]) ).
cnf(p228,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p226]) ).
cnf(f6,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f6_nnf,plain,
~ equalish(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ equalish(e_2,e_1),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p229,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p228,c6]) ).
cnf(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p230,plain,
$false,
inference(resolution,[status(thm)],[p229,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n011.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 13:47:32 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------