%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:25:23 PM UTC 2026
% Result : Unsatisfiable 22.26s 5.68s
% Output : Proof 22.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 11
% Syntax : Number of formulae : 165 ( 23 unt; 0 def)
% Number of atoms : 708 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 635 ( 92 ~; 543 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 101 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,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(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c9,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)],[f9_sk]) ).
cnf(f1,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f1_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p19,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)],[c9,c1]) ).
cnf(f0,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f0_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p38,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)],[p19,c0]) ).
cnf(p17,plain,
( product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c9]) ).
cnf(p22,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)],[p17,c0]) ).
cnf(f12,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f12_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p33,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,c12]) ).
cnf(p138,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p38,p33]) ).
cnf(p23,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p17,c1]) ).
cnf(f13,negated_conjecture,
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f13_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,X)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p14,plain,
( product(X1,X1,X0)
| ~ product(X0,X0,X1) ),
inference(factoring,[status(thm)],[c13]) ).
cnf(p54,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p23,p14]) ).
cnf(f10,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f10_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p61,plain,
( equalish(e_2,X0)
| ~ product(e_3,e_3,X0)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p54,c10]) ).
cnf(p28,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,p14]) ).
cnf(p66,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p61,p28]) ).
cnf(f11,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f11_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p110,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p66,c11]) ).
cnf(p306,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(factoring,[status(thm)],[p110]) ).
cnf(p465,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p138,p306]) ).
cnf(p1569,plain,
( product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p465]) ).
cnf(p1677,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p1569]) ).
cnf(p1679,plain,
( product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p1677,p14]) ).
cnf(p1687,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p1679]) ).
cnf(p31,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,c11]) ).
cnf(p18,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)],[c9,c0]) ).
cnf(p25,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)],[p18,c1]) ).
cnf(p105,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p31,p25]) ).
cnf(p111,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p66,c12]) ).
cnf(p307,plain,
( ~ product(e_1,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(factoring,[status(thm)],[p111]) ).
cnf(p402,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p105,p307]) ).
cnf(p1121,plain,
( product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p402]) ).
cnf(p1571,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1121]) ).
cnf(p1573,plain,
( product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1571,p14]) ).
cnf(p1577,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1573]) ).
cnf(p1578,plain,
( product(e_1,X0,e_1)
| ~ product(e_2,e_1,X0)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1577,c13]) ).
cnf(p1593,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1578]) ).
cnf(p1693,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1687,p1593]) ).
cnf(p2450,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1693]) ).
cnf(p2454,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2450]) ).
cnf(p2457,plain,
( equalish(e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2454]) ).
cnf(p2459,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2457]) ).
cnf(p130,plain,
( product(e_3,X0,e_2)
| ~ product(e_1,e_2,X0)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p38,c13]) ).
cnf(p145,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_3,e_3,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p130,p25]) ).
cnf(p184,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p145,p14]) ).
cnf(p195,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p184,c11]) ).
cnf(p382,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p195,p38]) ).
cnf(p640,plain,
( product(e_2,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p382]) ).
cnf(p642,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p640]) ).
cnf(p646,plain,
( equalish(e_2,X0)
| ~ product(X0,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p642,c12]) ).
cnf(p655,plain,
( ~ product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(factoring,[status(thm)],[p646]) ).
cnf(p2470,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2459,p655]) ).
cnf(p2600,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2470]) ).
cnf(p2461,plain,
( product(e_2,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2459,p14]) ).
cnf(p2477,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2461,c11]) ).
cnf(p2510,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2477]) ).
cnf(p2607,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2600,p2510]) ).
cnf(p4709,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2607]) ).
cnf(p4712,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4709]) ).
cnf(p4714,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4712]) ).
cnf(p2463,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2459,c11]) ).
cnf(p2487,plain,
( ~ product(e_1,e_2,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2463]) ).
cnf(p4725,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p4714,p2487]) ).
cnf(p4740,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)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4725]) ).
cnf(p4743,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4740]) ).
cnf(p4745,plain,
( product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4743]) ).
cnf(p2478,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2461,c12]) ).
cnf(p2517,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2478]) ).
cnf(p4752,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p4745,p2517]) ).
cnf(p4755,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4752]) ).
cnf(p4758,plain,
( equalish(e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4755]) ).
cnf(p4760,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4758]) ).
cnf(p4765,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)],[p4760,c12]) ).
cnf(p4787,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4765]) ).
cnf(p78,plain,
( equalish(e_1,X0)
| ~ product(X0,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p25,c12]) ).
cnf(p364,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p78,p23]) ).
cnf(p365,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p78,p184]) ).
cnf(p523,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p365]) ).
cnf(p525,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p523]) ).
cnf(p528,plain,
( equalish(e_1,X0)
| ~ product(e_2,X0,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p525,c11]) ).
cnf(p533,plain,
( ~ product(e_2,e_2,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p528]) ).
cnf(p925,plain,
( product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p364,p533]) ).
cnf(p4041,plain,
( product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p925]) ).
cnf(p4336,plain,
( product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p4041]) ).
cnf(p4338,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p4336]) ).
cnf(p4340,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p4338,p14]) ).
cnf(p4799,plain,
( product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p4787,p4340]) ).
cnf(p4833,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4799]) ).
cnf(p4846,plain,
( equalish(e_1,X0)
| ~ product(X0,e_2,e_2)
| product(e_1,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)],[p4833,c12]) ).
cnf(p4863,plain,
( ~ product(e_2,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4846]) ).
cnf(f2,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f2_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p20,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)],[c9,c2]) ).
cnf(p48,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p20,c1]) ).
cnf(p232,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p48,c12]) ).
cnf(p637,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p232,p23]) ).
cnf(p62,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p54,c11]) ).
cnf(p2612,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p637,p62]) ).
cnf(p2673,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p2612]) ).
cnf(p2676,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p2673]) ).
cnf(p2677,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p2676]) ).
cnf(p39,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)],[p19,c2]) ).
cnf(p142,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p39,c11]) ).
cnf(p490,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p142,p23]) ).
cnf(p63,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p54,c12]) ).
cnf(p1762,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p490,p63]) ).
cnf(p1803,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p1762]) ).
cnf(p1806,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p1803]) ).
cnf(p1808,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p1806]) ).
cnf(p1809,plain,
( product(e_1,X0,e_2)
| ~ product(e_3,e_2,X0)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p1808,c13]) ).
cnf(p2687,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2677,p1809]) ).
cnf(p2701,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_2)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2687]) ).
cnf(p2704,plain,
( product(e_1,e_1,e_2)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2701]) ).
cnf(p2705,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2704]) ).
cnf(p4889,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,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)],[p4863,p2705]) ).
cnf(p5021,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4889]) ).
cnf(p5023,plain,
( product(e_1,e_1,e_2)
| equalish(e_3,e_2)
| product(e_1,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)],[p5021,p14]) ).
cnf(p5030,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p5023]) ).
cnf(p4764,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)],[p4760,c11]) ).
cnf(p4786,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4764]) ).
cnf(p5046,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p5030,p4786]) ).
cnf(p5047,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p5046]) ).
cnf(p5049,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p5047]) ).
cnf(p4762,plain,
( equalish(e_1,X0)
| ~ product(e_1,e_1,X0)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p4760,c10]) ).
cnf(p4783,plain,
( ~ product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4762]) ).
cnf(p5067,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p5049,p4783]) ).
cnf(p5084,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p5067]) ).
cnf(p5086,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p5084]) ).
cnf(f8,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f8_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p5087,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p5086,c8]) ).
cnf(f5,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f5_nnf,plain,
~ equalish(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ equalish(e_2,e_1),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p5088,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p5087,c5]) ).
cnf(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f3_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p5089,plain,
$false,
inference(resolution,[status(thm)],[p5088,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 13:48:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.26/5.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.26/5.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------