%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP127-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:25:19 PM UTC 2026
% Result : Unsatisfiable 23.09s 3.48s
% Output : Proof 23.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 14
% Syntax : Number of formulae : 143 ( 20 unt; 0 def)
% Number of atoms : 478 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 444 ( 109 ~; 335 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 158 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
fof(f1_nnf,plain,
! [X,Y] :
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( product(X0,e_4,X1)
| product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f7,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f7_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p36,plain,
( product(e_4,e_4,X0)
| product(e_4,e_3,X0)
| product(e_4,e_2,X0)
| product(e_4,e_1,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(f6,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f6_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p124,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p36,c6]) ).
cnf(f2,negated_conjecture,
( ~ product(Z1,Y,Z2)
| ~ product(Z2,Y,X)
| product(Y,X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
fof(f2_nnf,plain,
! [Y,X,Z1,Z2] :
( ~ product(Z1,Y,Z2)
| ~ product(Z2,Y,X)
| product(Y,X,Z1) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Y,X,Z1,Z2] :
( ~ product(Z1,Y,Z2)
| ~ product(Z2,Y,X)
| product(Y,X,Z1) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ product(X2,X0,X3)
| ~ product(X3,X0,X1)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p907,plain,
( ~ product(X0,e_4,e_4)
| product(e_4,e_3,X0)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p124,c2]) ).
cnf(f24,axiom,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f24_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p4839,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p907,c24]) ).
cnf(f22,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f22_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p4858,plain,
( equalish(e_3,X0)
| ~ product(e_4,X0,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p4839,c22]) ).
cnf(p4910,plain,
( equalish(e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p4858,c24]) ).
cnf(f23,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f23_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p48,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c23,c24]) ).
cnf(p4929,plain,
( equalish(e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p4910,p48]) ).
cnf(p4946,plain,
( equalish(e_3,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(factoring,[status(thm)],[p4929]) ).
cnf(f3,negated_conjecture,
( ~ product(Y,X,Z1)
| ~ product(Z2,Y,X)
| product(Z1,Y,Z2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
fof(f3_nnf,plain,
! [Z1,Y,Z2,X] :
( ~ product(Y,X,Z1)
| ~ product(Z2,Y,X)
| product(Z1,Y,Z2) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Z1,Y,Z2,X] :
( ~ product(Y,X,Z1)
| ~ product(Z2,Y,X)
| product(Z1,Y,Z2) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ product(X1,X3,X0)
| ~ product(X2,X1,X3)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p4948,plain,
( ~ product(e_2,e_3,X0)
| product(X0,e_2,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p4946,c3]) ).
cnf(f0,axiom,
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f0_nnf,plain,
! [X,Y] :
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( product(e_4,X0,X1)
| product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p30,plain,
( product(e_4,e_3,X0)
| product(e_3,e_3,X0)
| product(e_2,e_3,X0)
| product(e_1,e_3,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(p69,plain,
( product(e_4,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p30,c7]) ).
cnf(p26,plain,
( ~ product(X1,X0,X1)
| product(X0,X1,X1) ),
inference(factoring,[status(thm)],[c2]) ).
cnf(p328,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p69,p26]) ).
cnf(p343,plain,
( equalish(e_3,X0)
| ~ product(X0,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p328,c23]) ).
cnf(p368,plain,
( equalish(e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p343,c24]) ).
cnf(f21,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f21_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p45,plain,
( equalish(X0,X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c21,c24]) ).
cnf(p375,plain,
( equalish(e_3,e_4)
| equalish(e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p368,p45]) ).
cnf(p381,plain,
( equalish(e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(factoring,[status(thm)],[p375]) ).
cnf(p5025,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_2,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p4948,p381]) ).
cnf(p5152,plain,
( product(e_1,e_3,e_4)
| product(e_4,e_2,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(factoring,[status(thm)],[p5025]) ).
cnf(p4950,plain,
( equalish(e_3,X0)
| ~ product(e_4,e_2,X0)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p4946,c21]) ).
cnf(p4986,plain,
( ~ product(e_4,e_2,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(factoring,[status(thm)],[p4950]) ).
cnf(p5192,plain,
( equalish(e_3,e_4)
| product(e_4,e_1,e_3)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p5152,p4986]) ).
cnf(p5486,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(factoring,[status(thm)],[p5192]) ).
cnf(p5488,plain,
( product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(factoring,[status(thm)],[p5486]) ).
cnf(f20,axiom,
( product(X,Y,e_4)
| 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(f20_nnf,plain,
! [X,Y] :
( product(X,Y,e_4)
| 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)],[f20]) ).
fof(f20_sk,plain,
! [X,Y] :
( product(X,Y,e_4)
| 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)],[f20_nnf]) ).
cnf(c20,plain,
( product(X0,X1,e_4)
| 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)],[f20_sk]) ).
cnf(p42,plain,
( product(e_3,X0,e_4)
| 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)],[c20,c6]) ).
cnf(p192,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p42,c7]) ).
cnf(p37,plain,
( ~ product(X1,X0,X0)
| product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c24,c2]) ).
cnf(p1727,plain,
( product(e_4,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p192,p37]) ).
cnf(p1752,plain,
( equalish(e_3,X0)
| ~ product(e_4,e_4,X0)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1727,c21]) ).
cnf(p1772,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1752,c24]) ).
cnf(p47,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c22,c24]) ).
cnf(p1789,plain,
( equalish(e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1772,p47]) ).
cnf(p1802,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p1789]) ).
cnf(f25,negated_conjecture,
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f25_nnf,plain,
! [Y,X,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Y,X,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p1805,plain,
( product(X0,e_3,e_4)
| ~ product(e_2,e_3,X0)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1802,c25]) ).
cnf(p1852,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_4,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1805,p381]) ).
cnf(p1947,plain,
( product(e_1,e_3,e_4)
| product(e_4,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p1852]) ).
cnf(p1967,plain,
( equalish(e_3,X0)
| ~ product(e_4,X0,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1947,c22]) ).
cnf(p2314,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1967,c24]) ).
cnf(p2319,plain,
( product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p2314]) ).
cnf(p2329,plain,
( ~ product(e_4,e_1,X0)
| product(X0,e_4,e_3)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p2319,c3]) ).
cnf(p5503,plain,
( product(e_3,e_4,e_3)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5488,p2329]) ).
cnf(p5834,plain,
( product(e_3,e_4,e_3)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p5503]) ).
cnf(p5835,plain,
( product(e_3,e_4,e_3)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p5834]) ).
cnf(p5842,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5835,p47]) ).
cnf(p5855,plain,
( product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p5842]) ).
cnf(p31,plain,
( product(e_4,e_4,X0)
| product(e_3,e_4,X0)
| product(e_2,e_4,X0)
| product(e_1,e_4,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(p90,plain,
( product(e_4,e_4,e_3)
| product(e_3,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[p31,c6]) ).
cnf(p38,plain,
( ~ product(X1,X1,X0)
| product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c24,c3]) ).
cnf(p525,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[p90,p38]) ).
cnf(p540,plain,
( equalish(e_3,X0)
| ~ product(X0,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[p525,c23]) ).
cnf(p561,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[p540,c24]) ).
cnf(p583,plain,
( equalish(e_3,e_4)
| equalish(e_3,e_4)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[p561,p47]) ).
cnf(p590,plain,
( equalish(e_3,e_4)
| product(e_2,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(factoring,[status(thm)],[p583]) ).
cnf(p591,plain,
( ~ product(X0,e_4,e_2)
| product(e_4,e_3,X0)
| equalish(e_3,e_4)
| product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[p590,c2]) ).
cnf(p1813,plain,
( product(e_4,e_3,e_3)
| equalish(e_3,e_4)
| product(e_1,e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1802,p591]) ).
cnf(p1873,plain,
( product(e_4,e_3,e_3)
| product(e_1,e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p1813]) ).
cnf(p1887,plain,
( equalish(e_3,e_4)
| product(e_1,e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1873,p48]) ).
cnf(p1897,plain,
( product(e_1,e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p1887]) ).
cnf(p1900,plain,
( product(X0,e_3,e_4)
| ~ product(e_1,e_3,X0)
| product(e_1,e_4,e_3)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p1897,c25]) ).
cnf(p5877,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_4,e_3)
| equalish(e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5855,p1900]) ).
cnf(p5925,plain,
( product(e_4,e_3,e_4)
| product(e_1,e_4,e_3)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p5877]) ).
cnf(p5931,plain,
( equalish(e_3,X0)
| ~ product(e_4,X0,e_4)
| product(e_1,e_4,e_3)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5925,c22]) ).
cnf(p6147,plain,
( equalish(e_3,e_4)
| product(e_1,e_4,e_3)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5931,c24]) ).
cnf(p6150,plain,
( product(e_1,e_4,e_3)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p6147]) ).
cnf(p6151,plain,
( ~ product(X0,e_4,e_1)
| product(e_4,e_3,X0)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6150,c2]) ).
cnf(p5866,plain,
( ~ product(e_3,e_4,X0)
| product(X0,e_3,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5855,c3]) ).
cnf(p5901,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5866,p1802]) ).
cnf(p6071,plain,
( product(e_3,e_4,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p5901]) ).
cnf(p6204,plain,
( product(e_2,e_3,e_1)
| equalish(e_3,e_4)
| product(e_4,e_3,e_3)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6151,p6071]) ).
cnf(p6293,plain,
( product(e_2,e_3,e_1)
| product(e_4,e_3,e_3)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p6204]) ).
cnf(p6301,plain,
( equalish(e_3,e_4)
| product(e_2,e_3,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6293,p48]) ).
cnf(p6322,plain,
( product(e_2,e_3,e_1)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p6301]) ).
cnf(p5865,plain,
( ~ product(X0,e_3,e_1)
| product(e_3,e_4,X0)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5855,c2]) ).
cnf(p6337,plain,
( product(e_3,e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6322,p5865]) ).
cnf(p6348,plain,
( product(e_3,e_4,e_2)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p6337]) ).
cnf(p6349,plain,
( ~ product(X0,e_4,e_3)
| product(e_4,e_2,X0)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6348,c2]) ).
cnf(p6433,plain,
( equalish(e_3,e_4)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6349,p6150]) ).
cnf(p6443,plain,
( product(e_4,e_2,e_1)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p6433]) ).
cnf(p6459,plain,
( equalish(e_3,e_1)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6443,p4950]) ).
cnf(p6499,plain,
( equalish(e_3,e_1)
| product(e_4,e_1,e_3)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p6459]) ).
cnf(p5867,plain,
( product(X0,e_1,e_3)
| ~ product(e_4,e_1,X0)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p5855,c25]) ).
cnf(p6516,plain,
( product(e_3,e_1,e_3)
| equalish(e_3,e_4)
| equalish(e_3,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6499,p5867]) ).
cnf(p6552,plain,
( product(e_3,e_1,e_3)
| equalish(e_3,e_1)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p6516]) ).
cnf(p6568,plain,
( equalish(e_3,e_1)
| equalish(e_3,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p6552,p47]) ).
cnf(p6583,plain,
( equalish(e_3,e_1)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p6568]) ).
cnf(f16,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f16_nnf,plain,
~ equalish(e_3,e_4),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
~ equalish(e_3,e_4),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p6584,plain,
equalish(e_3,e_1),
inference(resolution,[status(thm)],[p6583,c16]) ).
cnf(f14,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f14_nnf,plain,
~ equalish(e_3,e_1),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ equalish(e_3,e_1),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p6585,plain,
$false,
inference(resolution,[status(thm)],[p6584,c14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP127-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:45:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.09/3.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.09/3.48 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------