%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP129-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:25:20 PM UTC 2026
% Result : Unsatisfiable 15.91s 4.84s
% Output : Proof 15.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 122
% Number of leaves : 11
% Syntax : Number of formulae : 238 ( 23 unt; 0 def)
% Number of atoms : 1106 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 980 ( 112 ~; 868 |; 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 : 113 ( 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(p16,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(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(p23,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p16,c2]) ).
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(p64,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p23,c12]) ).
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(p18,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(p43,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)],[p18,c2]) ).
cnf(p208,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p64,p43]) ).
cnf(f13,negated_conjecture,
( product(Z1,Y,Z2)
| ~ product(X,Z1,Z2)
| ~ product(Y,X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f13_nnf,plain,
! [Y,X,Z1,Z2] :
( product(Z1,Y,Z2)
| ~ product(X,Z1,Z2)
| ~ product(Y,X,Z1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y,X,Z1,Z2] :
( product(Z1,Y,Z2)
| ~ product(X,Z1,Z2)
| ~ product(Y,X,Z1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( product(X2,X0,X3)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p897,plain,
( product(e_2,e_3,X0)
| ~ product(e_3,e_2,X0)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p208,c13]) ).
cnf(p940,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(factoring,[status(thm)],[p897]) ).
cnf(p19,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(p47,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)],[p19,c1]) ).
cnf(p146,plain,
( product(e_3,e_3,X0)
| ~ product(e_2,e_3,X0)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p47,c13]) ).
cnf(p151,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p146,p43]) ).
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(p153,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p151,c11]) ).
cnf(p201,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p153,p47]) ).
cnf(p421,plain,
( product(e_3,e_2,e_2)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p201]) ).
cnf(p424,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p421]) ).
cnf(p949,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p940,p424]) ).
cnf(p2683,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(factoring,[status(thm)],[p949]) ).
cnf(p2686,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(factoring,[status(thm)],[p2683]) ).
cnf(p2698,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(factoring,[status(thm)],[p2686]) ).
cnf(p110,plain,
( product(e_3,e_2,X0)
| ~ product(e_3,e_3,X0)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p43,c13]) ).
cnf(p2704,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2698,p110]) ).
cnf(p2717,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2704]) ).
cnf(p2720,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2717]) ).
cnf(p2722,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2720]) ).
cnf(p939,plain,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(factoring,[status(thm)],[p897]) ).
cnf(p2737,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2722,p939]) ).
cnf(p2789,plain,
( product(e_2,e_3,e_2)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2737]) ).
cnf(p2792,plain,
( equalish(e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2789]) ).
cnf(p2793,plain,
( product(e_3,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2792]) ).
cnf(p2798,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2793,c11]) ).
cnf(p2805,plain,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2798]) ).
cnf(p2812,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2805,p2722]) ).
cnf(p2821,plain,
( product(e_2,e_3,e_2)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2812]) ).
cnf(p2824,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2821]) ).
cnf(p2827,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2824]) ).
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(p17,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(p30,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)],[p17,c1]) ).
cnf(p79,plain,
( product(e_3,e_1,X0)
| ~ product(e_2,e_3,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p30,c13]) ).
cnf(p2832,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2827,p79]) ).
cnf(p2920,plain,
( product(e_2,e_3,X0)
| ~ product(e_1,e_2,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2832,c13]) ).
cnf(p3161,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2920,p30]) ).
cnf(p3466,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_3,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3161]) ).
cnf(p3468,plain,
( product(e_2,e_3,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3466]) ).
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(p3470,plain,
( equalish(e_3,X0)
| ~ product(e_2,e_3,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3468,c10]) ).
cnf(p3482,plain,
( ~ product(e_2,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3470]) ).
cnf(p3490,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_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3482,p2827]) ).
cnf(p3497,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3490]) ).
cnf(p3498,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3497]) ).
cnf(p3503,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3498,p79]) ).
cnf(p3570,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3503]) ).
cnf(p3574,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3570]) ).
cnf(p3499,plain,
( product(e_1,e_2,X0)
| ~ product(e_3,e_1,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3498,c13]) ).
cnf(p3542,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3499]) ).
cnf(p3584,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3574,p3542]) ).
cnf(p3591,plain,
( product(e_1,e_2,e_2)
| equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3584]) ).
cnf(p3596,plain,
( equalish(e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3591]) ).
cnf(p3597,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3596]) ).
cnf(p3598,plain,
( product(e_2,e_1,X0)
| ~ product(e_2,e_2,X0)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3597,c13]) ).
cnf(p22,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)],[p16,c1]) ).
cnf(p3673,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3598,p22]) ).
cnf(p3684,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3673,c12]) ).
cnf(p3782,plain,
( product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3684,p3597]) ).
cnf(p4013,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3782]) ).
cnf(p4016,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4013]) ).
cnf(p4028,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4016,p3598]) ).
cnf(p4176,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4028]) ).
cnf(p4183,plain,
( product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4176]) ).
cnf(p55,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p22,c11]) ).
cnf(p4189,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4183,p55]) ).
cnf(p4388,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4189]) ).
cnf(p4391,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4388,c12]) ).
cnf(p4467,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4391]) ).
cnf(p4470,plain,
( product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4467,p3597]) ).
cnf(p4492,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4470]) ).
cnf(p4493,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4492]) ).
cnf(p4504,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4493,p3598]) ).
cnf(p4547,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_2)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4504]) ).
cnf(p4554,plain,
( equalish(e_3,e_2)
| product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4547]) ).
cnf(p4555,plain,
( product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4554]) ).
cnf(p4019,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| equalish(e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4016,c11]) ).
cnf(p4034,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4019]) ).
cnf(p4573,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4555,p4034]) ).
cnf(p4876,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4573]) ).
cnf(p4878,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4876]) ).
cnf(p4882,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4878]) ).
cnf(p4887,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4882,p55]) ).
cnf(p4911,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4887]) ).
cnf(p4914,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4911,c12]) ).
cnf(p4935,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4914]) ).
cnf(p4938,plain,
( product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4935,p3597]) ).
cnf(p4964,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4938]) ).
cnf(p4965,plain,
( product(e_2,e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4964]) ).
cnf(p4968,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4965,c11]) ).
cnf(p4986,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4968]) ).
cnf(p4988,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4986,p4555]) ).
cnf(p4993,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4988]) ).
cnf(p4995,plain,
( equalish(e_2,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4993]) ).
cnf(p4997,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4995]) ).
cnf(p5000,plain,
( product(e_1,e_1,X0)
| ~ product(e_2,e_1,X0)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4997,c13]) ).
cnf(p42,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)],[p18,c0]) ).
cnf(p5024,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5000,p42]) ).
cnf(p5029,plain,
( product(e_2,e_2,X0)
| ~ product(e_1,e_2,X0)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5024,c13]) ).
cnf(p5145,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5029,p4997]) ).
cnf(p5199,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5145]) ).
cnf(p5205,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5199]) ).
cnf(p5209,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5205,c12]) ).
cnf(p5225,plain,
( ~ product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5209]) ).
cnf(p5227,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5225,p4997]) ).
cnf(p5228,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5227]) ).
cnf(p5230,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5228]) ).
cnf(p2833,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2827,p146]) ).
cnf(p2934,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2833,c12]) ).
cnf(p3035,plain,
( ~ product(e_2,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2934]) ).
cnf(p3045,plain,
( product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3035,p2827]) ).
cnf(p3076,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3045]) ).
cnf(p3077,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3076]) ).
cnf(p3081,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3077,c12]) ).
cnf(p3625,plain,
( equalish(e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3597,p3081]) ).
cnf(p3702,plain,
( equalish(e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3625]) ).
cnf(p2828,plain,
( product(e_2,e_2,X0)
| ~ product(e_3,e_2,X0)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2827,c13]) ).
cnf(p3721,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3702,p2828]) ).
cnf(p3937,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3721]) ).
cnf(p3938,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3937]) ).
cnf(p3941,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_1)
| product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3938,c11]) ).
cnf(p3955,plain,
( ~ product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p3941]) ).
cnf(p4571,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4555,p3955]) ).
cnf(p4664,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4571]) ).
cnf(p4665,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4664]) ).
cnf(p4669,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4665,c11]) ).
cnf(p4677,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4669]) ).
cnf(p4679,plain,
( equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4677,p4555]) ).
cnf(p4682,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4679]) ).
cnf(p4684,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4682]) ).
cnf(p4691,plain,
( equalish(e_3,e_1)
| equalish(e_2,e_1)
| product(e_1,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4684]) ).
cnf(p52,plain,
( product(e_3,e_2,X0)
| ~ product(e_2,e_3,X0)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p22,c13]) ).
cnf(p114,plain,
( product(e_3,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p43,p52]) ).
cnf(p121,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p114,c12]) ).
cnf(p169,plain,
( 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)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p121,p22]) ).
cnf(p281,plain,
( 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)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p169]) ).
cnf(p283,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p281]) ).
cnf(p289,plain,
( product(e_3,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_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p283,p52]) ).
cnf(p533,plain,
( product(e_3,e_2,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)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p289]) ).
cnf(p537,plain,
( product(e_3,e_2,e_2)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p533]) ).
cnf(p538,plain,
( product(e_2,e_3,X0)
| ~ product(e_2,e_2,X0)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p537,c13]) ).
cnf(p557,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_3)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p538,p22]) ).
cnf(p800,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_3,e_3)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p557]) ).
cnf(p813,plain,
( product(e_2,e_3,e_3)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p800]) ).
cnf(p816,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_3)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p813,c11]) ).
cnf(p838,plain,
( ~ product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p816]) ).
cnf(p841,plain,
( 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)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p838,p22]) ).
cnf(p852,plain,
( 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)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p841]) ).
cnf(p854,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p852]) ).
cnf(p859,plain,
( product(e_3,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_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p854,p52]) ).
cnf(p888,plain,
( product(e_3,e_2,e_1)
| 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) ),
inference(factoring,[status(thm)],[p859]) ).
cnf(p890,plain,
( product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(factoring,[status(thm)],[p888]) ).
cnf(p894,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p890,c12]) ).
cnf(p4700,plain,
( equalish(e_3,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_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4691,p894]) ).
cnf(p4733,plain,
( equalish(e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4700]) ).
cnf(p4735,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4733]) ).
cnf(p2830,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p2827,c11]) ).
cnf(p2852,plain,
( ~ product(e_2,e_2,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p2830]) ).
cnf(p4742,plain,
( product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4735,p2852]) ).
cnf(p4761,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4742]) ).
cnf(p4764,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_1)
| product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4761,c11]) ).
cnf(p4774,plain,
( ~ product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4764]) ).
cnf(p5239,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5230,p4774]) ).
cnf(p5337,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5239]) ).
cnf(p5339,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5337]) ).
cnf(p5343,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5339,c12]) ).
cnf(p5354,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5343]) ).
cnf(p5356,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5354,p4997]) ).
cnf(p5360,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5356]) ).
cnf(p5362,plain,
( equalish(e_3,e_1)
| product(e_1,e_1,e_3)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5360]) ).
cnf(p103,plain,
( equalish(e_2,X0)
| ~ product(X0,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p42,c12]) ).
cnf(p5368,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5362,p103]) ).
cnf(p5397,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5368]) ).
cnf(p5398,plain,
( product(e_2,e_2,X0)
| ~ product(e_1,e_2,X0)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5397,c13]) ).
cnf(p5460,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5398,p4997]) ).
cnf(p5527,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5460]) ).
cnf(p5529,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5527]) ).
cnf(p5533,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5529,c12]) ).
cnf(p5543,plain,
( ~ product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5533]) ).
cnf(p5545,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5543,p4997]) ).
cnf(p5548,plain,
( equalish(e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5545]) ).
cnf(p5550,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5548]) ).
cnf(p5559,plain,
( product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5550,p5000]) ).
cnf(p5573,plain,
( product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5559]) ).
cnf(p5576,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5573]) ).
cnf(p5002,plain,
( equalish(e_2,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4997,c11]) ).
cnf(p5016,plain,
( ~ product(e_1,e_1,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5002]) ).
cnf(p5581,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p5576,p5016]) ).
cnf(p5582,plain,
( equalish(e_2,e_1)
| equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5581]) ).
cnf(p5584,plain,
( equalish(e_3,e_1)
| equalish(e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5582]) ).
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(p5585,plain,
( equalish(e_3,e_1)
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[p5584,c8]) ).
cnf(f7,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f7_nnf,plain,
~ equalish(e_3,e_1),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ equalish(e_3,e_1),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p5586,plain,
equalish(e_2,e_1),
inference(resolution,[status(thm)],[p5585,c7]) ).
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(p5587,plain,
$false,
inference(resolution,[status(thm)],[p5586,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP129-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Wed Sep 23 13:44:35 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.91/4.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.91/4.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------