%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP130-3.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 01:25:21 PM UTC 2026
% Result : Unsatisfiable 29.76s 10.06s
% Output : Proof 29.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 20
% Syntax : Number of formulae : 209 ( 44 unt; 0 def)
% Number of atoms : 776 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 709 ( 142 ~; 567 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 132 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,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/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f25_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)],[f25]) ).
fof(f25_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)],[f25_nnf]) ).
cnf(c25,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)],[f25_sk]) ).
cnf(f18,axiom,
group_element(e_3),
file('/export/starexec/sandbox/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(p61,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)],[c25,c18]) ).
cnf(f16,axiom,
group_element(e_1),
file('/export/starexec/sandbox/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(p173,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)],[p61,c16]) ).
cnf(p59,plain,
( product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c25,c16]) ).
cnf(p154,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p59,c18]) ).
cnf(f29,negated_conjecture,
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f29_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p30,plain,
( product(X1,X1,X0)
| ~ product(X0,X1,X1) ),
inference(factoring,[status(thm)],[c29]) ).
cnf(p163,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p154,p30]) ).
cnf(p169,plain,
( product(X0,e_3,e_3)
| ~ product(e_3,e_1,X0)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p163,c29]) ).
cnf(p464,plain,
( product(e_3,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p173,p169]) ).
cnf(f26,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f26_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p170,plain,
( equalish(e_1,X0)
| ~ product(e_3,e_3,X0)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p163,c26]) ).
cnf(p475,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p464,p170]) ).
cnf(p928,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p475]) ).
cnf(p1014,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p928]) ).
cnf(p1025,plain,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p1014,p169]) ).
cnf(p3899,plain,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p1025]) ).
cnf(p3901,plain,
( product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p3899]) ).
cnf(f27,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f27_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p165,plain,
( equalish(e_3,X0)
| ~ product(e_1,X0,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p154,c27]) ).
cnf(p58,plain,
( product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c25]) ).
cnf(p66,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p58,c16]) ).
cnf(p69,plain,
( product(X0,e_1,e_1)
| ~ product(e_1,e_3,X0)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p66,c29]) ).
cnf(p167,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p154,p69]) ).
cnf(p171,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p163,c27]) ).
cnf(p181,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p167,p171]) ).
cnf(p193,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p181]) ).
cnf(p195,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p193]) ).
cnf(p200,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p195,p69]) ).
cnf(p225,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p200]) ).
cnf(p227,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p225]) ).
cnf(p229,plain,
( product(e_1,e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p227,p30]) ).
cnf(p234,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p229]) ).
cnf(p78,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p69]) ).
cnf(p240,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p234,p78]) ).
cnf(p245,plain,
( product(e_1,e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p240]) ).
cnf(p247,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p245]) ).
cnf(p248,plain,
( product(X0,e_1,e_1)
| ~ product(e_1,e_2,X0)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p247,c29]) ).
cnf(f17,axiom,
group_element(e_2),
file('/export/starexec/sandbox/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(p153,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p59,c17]) ).
cnf(p258,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_3,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p248,p153]) ).
cnf(p260,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p258,p30]) ).
cnf(p250,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p247,c27]) ).
cnf(p273,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p260,p250]) ).
cnf(p302,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p273]) ).
cnf(p304,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p302]) ).
cnf(p257,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p248]) ).
cnf(p310,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p304,p257]) ).
cnf(p312,plain,
( equalish(e_3,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p310]) ).
cnf(p314,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_3)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p312]) ).
cnf(p434,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p165,p314]) ).
cnf(p451,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p434]) ).
cnf(p454,plain,
( equalish(e_3,X0)
| ~ product(e_1,X0,e_2)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p451,c27]) ).
cnf(p578,plain,
( ~ product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p454]) ).
cnf(p580,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p578,p247]) ).
cnf(p596,plain,
( equalish(e_3,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p580]) ).
cnf(p597,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p596]) ).
cnf(p315,plain,
( product(X0,e_1,e_1)
| ~ product(e_1,e_3,X0)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p314,c29]) ).
cnf(p327,plain,
( ~ product(e_1,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p315]) ).
cnf(p609,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p597,p327]) ).
cnf(p616,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p609]) ).
cnf(p620,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p616]) ).
cnf(p622,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p620]) ).
cnf(f15,axiom,
( equalish(Z,X1)
| ~ next(X,X1)
| ~ greater(Y,e_0)
| ~ product(X,e_1,Z)
| ~ cycle(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle7) ).
fof(f15_nnf,plain,
! [X,Y,Z,X1] :
( equalish(Z,X1)
| ~ next(X,X1)
| ~ greater(Y,e_0)
| ~ product(X,e_1,Z)
| ~ cycle(X,Y) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,Z,X1] :
( equalish(Z,X1)
| ~ next(X,X1)
| ~ greater(Y,e_0)
| ~ product(X,e_1,Z)
| ~ cycle(X,Y) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( equalish(X2,X3)
| ~ next(X0,X3)
| ~ greater(X1,e_0)
| ~ product(X0,e_1,X2)
| ~ cycle(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f10,axiom,
( cycle(X,e_2)
| cycle(X,e_1)
| cycle(X,e_0)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle2) ).
fof(f10_nnf,plain,
! [X] :
( cycle(X,e_2)
| cycle(X,e_1)
| cycle(X,e_0)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] :
( cycle(X,e_2)
| cycle(X,e_1)
| cycle(X,e_0)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( cycle(X0,e_2)
| cycle(X0,e_1)
| cycle(X0,e_0)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p33,plain,
( cycle(e_1,e_2)
| cycle(e_1,e_1)
| cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[c10,c16]) ).
cnf(p54,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| equalish(X0,X1)
| ~ next(e_1,X1)
| ~ greater(e_2,e_0)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[c15,p33]) ).
cnf(p627,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| equalish(e_1,X0)
| ~ next(e_1,X0)
| ~ greater(e_2,e_0)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p622,p54]) ).
cnf(p643,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| ~ next(e_1,e_2)
| ~ greater(e_2,e_0)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(factoring,[status(thm)],[p627]) ).
cnf(f4,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_0) ).
fof(f4_nnf,plain,
greater(e_2,e_0),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
greater(e_2,e_0),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p645,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| ~ next(e_1,e_2)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p643,c4]) ).
cnf(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f1_nnf,plain,
next(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
next(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p646,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| equalish(e_1,e_2)
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[p645,c1]) ).
cnf(f23,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f23_nnf,plain,
~ equalish(e_3,e_1),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
~ equalish(e_3,e_1),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p647,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p646,c23]) ).
cnf(f19,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f19_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p648,plain,
( cycle(e_1,e_1)
| cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[p647,c19]) ).
cnf(p652,plain,
( equalish(X0,X1)
| ~ next(e_1,X1)
| ~ greater(e_1,e_0)
| ~ product(e_1,e_1,X0)
| cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[p648,c15]) ).
cnf(p667,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_1)
| equalish(e_1,X0)
| ~ next(e_1,X0)
| ~ greater(e_1,e_0)
| cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[p652,p622]) ).
cnf(p673,plain,
( equalish(e_3,e_1)
| equalish(e_1,e_2)
| ~ next(e_1,e_2)
| ~ greater(e_1,e_0)
| cycle(e_1,e_0) ),
inference(factoring,[status(thm)],[p667]) ).
cnf(f3,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_greater_e_0) ).
fof(f3_nnf,plain,
greater(e_1,e_0),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
greater(e_1,e_0),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(p675,plain,
( equalish(e_3,e_1)
| equalish(e_1,e_2)
| ~ next(e_1,e_2)
| cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[p673,c3]) ).
cnf(p676,plain,
( equalish(e_3,e_1)
| equalish(e_1,e_2)
| cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[p675,c1]) ).
cnf(p677,plain,
( equalish(e_1,e_2)
| cycle(e_1,e_0) ),
inference(resolution,[status(thm)],[p676,c23]) ).
cnf(p678,plain,
cycle(e_1,e_0),
inference(resolution,[status(thm)],[p677,c19]) ).
cnf(f14,axiom,
( ~ greater(Y,X)
| ~ product(X,e_1,Y)
| ~ cycle(X,e_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle6) ).
fof(f14_nnf,plain,
! [X,Y] :
( ~ greater(Y,X)
| ~ product(X,e_1,Y)
| ~ cycle(X,e_0) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y] :
( ~ greater(Y,X)
| ~ product(X,e_1,Y)
| ~ cycle(X,e_0) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ greater(X1,X0)
| ~ product(X0,e_1,X1)
| ~ cycle(X0,e_0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p682,plain,
( ~ greater(X0,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[p678,c14]) ).
cnf(p700,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ greater(e_3,e_1) ),
inference(resolution,[status(thm)],[p682,p66]) ).
cnf(f7,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
fof(f7_nnf,plain,
greater(e_3,e_1),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
greater(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p718,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p700,c7]) ).
cnf(p723,plain,
( ~ greater(e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p718,p682]) ).
cnf(f6,axiom,
greater(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).
fof(f6_nnf,plain,
greater(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
greater(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p724,plain,
product(e_1,e_1,e_1),
inference(resolution,[status(thm)],[p723,c6]) ).
cnf(f28,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f28_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p728,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[p724,c28]) ).
cnf(p3910,plain,
( equalish(e_1,e_3)
| product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p3901,p728]) ).
cnf(p3915,plain,
( product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p3910]) ).
cnf(p166,plain,
( equalish(e_1,X0)
| ~ product(X0,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p154,c28]) ).
cnf(p3925,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p3915,p166]) ).
cnf(p4006,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p3925]) ).
cnf(p4021,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4006]) ).
cnf(p4025,plain,
( equalish(e_1,X0)
| ~ product(X0,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4021,c28]) ).
cnf(p4048,plain,
( ~ product(e_3,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4025]) ).
cnf(p60,plain,
( product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c25,c17]) ).
cnf(p160,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p60,c18]) ).
cnf(p400,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p160,p30]) ).
cnf(p4073,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4048,p400]) ).
cnf(p4049,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4025]) ).
cnf(p4110,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4073,p4049]) ).
cnf(p4652,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4110]) ).
cnf(p4657,plain,
( equalish(e_1,e_2)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4652]) ).
cnf(p4659,plain,
( product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4657]) ).
cnf(p155,plain,
( product(X0,e_2,e_1)
| ~ product(e_1,e_3,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p153,c29]) ).
cnf(p168,plain,
( product(e_3,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p154,p155]) ).
cnf(p186,plain,
( equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p168,p171]) ).
cnf(p204,plain,
( equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p186]) ).
cnf(p206,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p204]) ).
cnf(p207,plain,
( product(X0,e_3,e_1)
| ~ product(e_1,e_2,X0)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p206,c29]) ).
cnf(p214,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_3,e_3,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p207,p153]) ).
cnf(p583,plain,
( product(e_1,e_2,e_2)
| product(e_3,e_3,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p214]) ).
cnf(p869,plain,
( product(e_3,e_3,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p583]) ).
cnf(p873,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p869,c28]) ).
cnf(p879,plain,
( ~ product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p873]) ).
cnf(p4667,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4659,p879]) ).
cnf(p5819,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4667]) ).
cnf(p727,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[p724,c27]) ).
cnf(p5826,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5819,p727]) ).
cnf(p5858,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5826]) ).
cnf(p5860,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5858,p30]) ).
cnf(p159,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p60,c16]) ).
cnf(p384,plain,
( equalish(e_1,X0)
| ~ product(e_2,X0,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p159,c27]) ).
cnf(p731,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p384,p160]) ).
cnf(p382,plain,
( product(X0,e_1,e_2)
| ~ product(e_2,e_3,X0)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p159,c29]) ).
cnf(p392,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p382]) ).
cnf(p1424,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_3,e_1)
| equalish(e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p731,p392]) ).
cnf(p1496,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_1)
| equalish(e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p1424]) ).
cnf(p1507,plain,
( product(e_2,e_3,e_1)
| equalish(e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p1496]) ).
cnf(p1514,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p1507,p382]) ).
cnf(p1599,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| equalish(e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p1514]) ).
cnf(p1601,plain,
( product(e_1,e_1,e_2)
| equalish(e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p1599]) ).
cnf(p1602,plain,
( product(X0,e_1,e_2)
| ~ product(e_2,e_2,X0)
| product(e_1,e_1,e_2)
| equalish(e_1,e_3)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p1601,c29]) ).
cnf(p1661,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_1,e_2)
| equalish(e_1,e_3)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p1602]) ).
cnf(p5882,plain,
( product(e_1,e_1,e_2)
| equalish(e_1,e_3)
| product(e_2,e_1,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5860,p1661]) ).
cnf(p5953,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5882]) ).
cnf(p5959,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5953,p728]) ).
cnf(p5965,plain,
( product(e_1,e_1,e_2)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5959]) ).
cnf(p5971,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| equalish(e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5965,p727]) ).
cnf(p5981,plain,
( product(e_1,e_1,e_2)
| equalish(e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p5971]) ).
cnf(p5986,plain,
( ~ greater(e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5981,p682]) ).
cnf(p6001,plain,
( equalish(e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p5986,c6]) ).
cnf(f24,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f24_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p6002,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p6001,c24]) ).
cnf(f20,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/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(p6003,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p6002,c20]) ).
cnf(p6004,plain,
$false,
inference(resolution,[status(thm)],[p6003,c19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP130-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/5.51 % Computer : n012.cluster.edu
% 0.03/5.51 % Model : x86_64 x86_64
% 0.03/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.51 % Memory : 8046.5625MB
% 0.03/5.51 % OS : Linux 6.8.0-71-generic
% 0.03/5.51 % CPULimit : 300
% 0.03/5.51 % WCLimit : 300
% 0.03/5.51 % DateTime : Wed Sep 23 13:47:00 UTC 2026
% 0.03/5.52 % CPUTime :
% 0.03/5.52 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 29.76/10.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.76/10.06 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------