%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 07:31:25 AM UTC 2026
% Result : Unsatisfiable 16.44s 7.82s
% Output : CNFRefutation 16.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 20
% Syntax : Number of formulae : 130 ( 130 unt; 0 def)
% Number of atoms : 130 ( 129 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 327 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos01,axiom,
! [VAR_0] : product(VAR_0,one) = VAR_0,
file('theBenchmark.p',sos01) ).
cnf(c_1,plain,
product(A,one) = A,
inference(clausify,[status(thm)],[sos01]) ).
fof(sos02,axiom,
! [VAR_0] : product(one,VAR_0) = VAR_0,
file('theBenchmark.p',sos02) ).
cnf(c_2,plain,
product(one,A) = A,
inference(clausify,[status(thm)],[sos02]) ).
fof(sos03,axiom,
! [VAR_0,VAR_1] : product(VAR_0,difference(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',sos03) ).
cnf(c_3,plain,
product(A,difference(A,B)) = B,
inference(clausify,[status(thm)],[sos03]) ).
fof(sos04,axiom,
! [VAR_0,VAR_1] : difference(VAR_0,product(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',sos04) ).
cnf(c_4,plain,
difference(A,product(A,B)) = B,
inference(clausify,[status(thm)],[sos04]) ).
fof(sos05,axiom,
! [VAR_0,VAR_1] : quotient(product(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',sos05) ).
cnf(c_5,plain,
quotient(product(A,B),B) = A,
inference(clausify,[status(thm)],[sos05]) ).
fof(sos06,axiom,
! [VAR_0,VAR_1] : product(quotient(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',sos06) ).
cnf(c_6,plain,
product(quotient(A,B),B) = A,
inference(clausify,[status(thm)],[sos06]) ).
fof(sos07,axiom,
! [VAR_0,VAR_1,VAR_2] : difference(VAR_0,product(product(VAR_0,VAR_1),VAR_2)) = quotient(product(VAR_1,product(VAR_2,VAR_0)),VAR_0),
file('theBenchmark.p',sos07) ).
cnf(c_7,plain,
difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A),
inference(clausify,[status(thm)],[sos07]) ).
fof(sos08,axiom,
! [VAR_0,VAR_1,VAR_2] : difference(product(VAR_0,VAR_1),product(VAR_0,product(VAR_1,VAR_2))) = quotient(quotient(product(VAR_2,product(VAR_0,VAR_1)),VAR_1),VAR_0),
file('theBenchmark.p',sos08) ).
cnf(c_8,plain,
difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A),
inference(clausify,[status(thm)],[sos08]) ).
fof(sos09,axiom,
! [VAR_0] : i(VAR_0) = difference(VAR_0,one),
file('theBenchmark.p',sos09) ).
cnf(c_9,plain,
i(A) = difference(A,one),
inference(clausify,[status(thm)],[sos09]) ).
fof(sos10,axiom,
! [VAR_0] : j(VAR_0) = quotient(one,VAR_0),
file('theBenchmark.p',sos10) ).
cnf(c_10,plain,
j(A) = quotient(one,A),
inference(clausify,[status(thm)],[sos10]) ).
fof(sos11,axiom,
! [VAR_0] : product(i(VAR_0),VAR_0) = product(VAR_0,j(VAR_0)),
file('theBenchmark.p',sos11) ).
cnf(c_11,plain,
product(i(A),A) = product(A,j(A)),
inference(clausify,[status(thm)],[sos11]) ).
cnf(c_6360,plain,
product(difference(A,one),A) = product(A,j(A)),
inference(paramod,[status(thm)],[c_9,c_11]) ).
cnf(c_12,plain,
product(difference(A,one),A) = product(A,quotient(one,A)),
inference(paramod,[status(thm)],[c_10,c_6360]) ).
fof(sos12,axiom,
! [VAR_0] : eta(VAR_0) = product(i(VAR_0),VAR_0),
file('theBenchmark.p',sos12) ).
cnf(c_13,plain,
eta(A) = product(i(A),A),
inference(clausify,[status(thm)],[sos12]) ).
cnf(c_6361,plain,
eta(A) = product(difference(A,one),A),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_14,plain,
eta(A) = product(A,quotient(one,A)),
inference(paramod,[status(thm)],[c_12,c_6361]) ).
fof(sos13,axiom,
! [VAR_0,VAR_1] : product(i(i(VAR_0)),VAR_1) = product(eta(VAR_0),product(VAR_0,VAR_1)),
file('theBenchmark.p',sos13) ).
cnf(c_15,plain,
product(i(i(A)),B) = product(eta(A),product(A,B)),
inference(clausify,[status(thm)],[sos13]) ).
cnf(c_6362,plain,
product(i(difference(A,one)),B) = product(eta(A),product(A,B)),
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_6363,plain,
product(difference(difference(A,one),one),B) = product(eta(A),product(A,B)),
inference(paramod,[status(thm)],[c_9,c_6362]) ).
cnf(c_6364,plain,
product(difference(difference(A,one),one),B) = product(product(A,quotient(one,A)),product(A,B)),
inference(paramod,[status(thm)],[c_14,c_6363]) ).
cnf(c_16,plain,
product(product(A,quotient(one,A)),product(A,B)) = product(difference(difference(A,one),one),B),
inference(copy,[status(thm)],[c_6364]) ).
fof(sos14,axiom,
! [VAR_0,VAR_1] : product(VAR_0,product(eta(VAR_0),VAR_1)) = product(j(j(VAR_0)),VAR_1),
file('theBenchmark.p',sos14) ).
cnf(c_17,plain,
product(A,product(eta(A),B)) = product(j(j(A)),B),
inference(clausify,[status(thm)],[sos14]) ).
cnf(c_6365,plain,
product(A,product(product(A,quotient(one,A)),B)) = product(j(j(A)),B),
inference(paramod,[status(thm)],[c_14,c_17]) ).
cnf(c_6366,plain,
product(A,product(product(A,quotient(one,A)),B)) = product(j(quotient(one,A)),B),
inference(paramod,[status(thm)],[c_10,c_6365]) ).
cnf(c_18,plain,
product(A,product(product(A,quotient(one,A)),B)) = product(quotient(one,quotient(one,A)),B),
inference(paramod,[status(thm)],[c_10,c_6366]) ).
fof(sos27,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : product(a(VAR_0,VAR_1,VAR_2),product(VAR_3,VAR_4)) = product(product(a(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),
file('theBenchmark.p',sos27) ).
cnf(c_39,plain,
product(a(A,B,C),product(D,E)) = product(product(a(A,B,C),D),E),
inference(clausify,[status(thm)],[sos27]) ).
cnf(c_40,plain,
product(product(a(A,B,C),D),E) = product(a(A,B,C),product(D,E)),
inference(copy,[status(thm)],[c_39]) ).
fof(sos29,axiom,
! [VAR_0,VAR_1,VAR_2] : product(a(VAR_0,VAR_1,VAR_2),difference(VAR_2,product(a(VAR_2,VAR_0,VAR_1),VAR_2))) = one,
file('theBenchmark.p',sos29) ).
cnf(c_42,plain,
product(a(A,B,C),difference(C,product(a(C,A,B),C))) = one,
inference(clausify,[status(thm)],[sos29]) ).
fof(sos30,axiom,
! [VAR_0,VAR_1,VAR_2] : a(VAR_0,i(VAR_1),VAR_2) = a(VAR_0,j(VAR_1),VAR_2),
file('theBenchmark.p',sos30) ).
cnf(c_43,plain,
a(A,i(B),C) = a(A,j(B),C),
inference(clausify,[status(thm)],[sos30]) ).
cnf(c_6367,plain,
a(A,difference(B,one),C) = a(A,j(B),C),
inference(paramod,[status(thm)],[c_9,c_43]) ).
cnf(c_44,plain,
a(A,difference(B,one),C) = a(A,quotient(one,B),C),
inference(paramod,[status(thm)],[c_10,c_6367]) ).
fof(sos31,axiom,
! [VAR_0,VAR_1,VAR_2] : a(i(VAR_0),VAR_1,VAR_2) = a(j(VAR_0),VAR_1,VAR_2),
file('theBenchmark.p',sos31) ).
cnf(c_45,plain,
a(i(A),B,C) = a(j(A),B,C),
inference(clausify,[status(thm)],[sos31]) ).
cnf(c_6368,plain,
a(difference(A,one),B,C) = a(j(A),B,C),
inference(paramod,[status(thm)],[c_9,c_45]) ).
cnf(c_46,plain,
a(difference(A,one),B,C) = a(quotient(one,A),B,C),
inference(paramod,[status(thm)],[c_10,c_6368]) ).
fof(sos32,axiom,
! [VAR_0,VAR_1,VAR_2] : a(j(VAR_0),VAR_1,VAR_2) = a(VAR_1,VAR_2,VAR_0),
file('theBenchmark.p',sos32) ).
cnf(c_47,plain,
a(j(A),B,C) = a(B,C,A),
inference(clausify,[status(thm)],[sos32]) ).
cnf(c_48,plain,
a(quotient(one,A),B,C) = a(B,C,A),
inference(paramod,[status(thm)],[c_10,c_47]) ).
fof(goals,axiom,
a(x0,x1,x1) != a(x1,x1,x0),
file('theBenchmark.p',goals) ).
cnf(c_49,plain,
a(x0,x1,x1) != a(x1,x1,x0),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_50,plain,
a(x1,x1,x0) != a(x0,x1,x1),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_53,plain,
a(difference(A,one),B,C) = a(B,C,A),
inference(paramod,[status(thm)],[c_48,c_46]) ).
cnf(c_55,plain,
difference(A,A) = one,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_58,plain,
quotient(A,difference(B,A)) = B,
inference(paramod,[status(thm)],[c_3,c_5]) ).
cnf(c_59,plain,
difference(quotient(A,B),A) = B,
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_6369,plain,
difference(A,product(B,C)) = quotient(product(difference(A,B),product(C,A)),A),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_61,plain,
quotient(product(difference(A,B),product(C,A)),A) = difference(A,product(B,C)),
inference(copy,[status(thm)],[c_6369]) ).
cnf(c_6370,plain,
difference(product(A,B),product(A,C)) = quotient(quotient(product(difference(B,C),product(A,B)),B),A),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_66,plain,
difference(product(A,B),product(A,C)) = quotient(difference(B,product(C,A)),A),
inference(paramod,[status(thm)],[c_61,c_6370]) ).
cnf(c_71,plain,
difference(difference(A,one),product(product(A,quotient(one,A)),B)) = quotient(product(A,product(B,difference(A,one))),difference(A,one)),
inference(paramod,[status(thm)],[c_12,c_7]) ).
cnf(c_6371,plain,
product(product(A,quotient(one,A)),A) = product(difference(difference(A,one),one),one),
inference(paramod,[status(thm)],[c_1,c_16]) ).
cnf(c_72,plain,
product(product(A,quotient(one,A)),A) = difference(difference(A,one),one),
inference(paramod,[status(thm)],[c_1,c_6371]) ).
cnf(c_6372,plain,
product(product(A,quotient(one,A)),B) = product(difference(difference(A,one),one),difference(A,B)),
inference(paramod,[status(thm)],[c_3,c_16]) ).
cnf(c_73,plain,
product(difference(difference(A,one),one),difference(A,B)) = product(product(A,quotient(one,A)),B),
inference(copy,[status(thm)],[c_6372]) ).
cnf(c_6373,plain,
product(A,product(A,quotient(one,A))) = product(quotient(one,quotient(one,A)),one),
inference(paramod,[status(thm)],[c_1,c_18]) ).
cnf(c_81,plain,
product(A,product(A,quotient(one,A))) = quotient(one,quotient(one,A)),
inference(paramod,[status(thm)],[c_1,c_6373]) ).
cnf(c_172,plain,
quotient(product(a(A,B,C),product(D,E)),E) = product(a(A,B,C),D),
inference(paramod,[status(thm)],[c_40,c_5]) ).
cnf(c_6374,plain,
difference(a(A,B,C),product(a(A,B,C),product(D,E))) = quotient(product(D,product(E,a(A,B,C))),a(A,B,C)),
inference(paramod,[status(thm)],[c_40,c_7]) ).
cnf(c_6375,plain,
product(D,E) = quotient(product(D,product(E,a(A,B,C))),a(A,B,C)),
inference(paramod,[status(thm)],[c_4,c_6374]) ).
cnf(c_174,plain,
quotient(product(A,product(B,a(C,D,E))),a(C,D,E)) = product(A,B),
inference(copy,[status(thm)],[c_6375]) ).
cnf(c_6376,plain,
difference(a(A,B,C),one) = difference(C,product(a(C,A,B),C)),
inference(paramod,[status(thm)],[c_42,c_4]) ).
cnf(c_196,plain,
difference(A,product(a(A,B,C),A)) = difference(a(B,C,A),one),
inference(copy,[status(thm)],[c_6376]) ).
cnf(c_6377,plain,
difference(a(A,B,C),product(one,D)) = quotient(product(difference(C,product(a(C,A,B),C)),product(D,a(A,B,C))),a(A,B,C)),
inference(paramod,[status(thm)],[c_42,c_7]) ).
cnf(c_6378,plain,
difference(a(A,B,C),D) = quotient(product(difference(C,product(a(C,A,B),C)),product(D,a(A,B,C))),a(A,B,C)),
inference(paramod,[status(thm)],[c_2,c_6377]) ).
cnf(c_6379,plain,
difference(a(A,B,C),D) = quotient(product(difference(a(A,B,C),one),product(D,a(A,B,C))),a(A,B,C)),
inference(paramod,[status(thm)],[c_196,c_6378]) ).
cnf(c_6380,plain,
difference(a(A,B,C),D) = product(difference(a(A,B,C),one),D),
inference(paramod,[status(thm)],[c_174,c_6379]) ).
cnf(c_197,plain,
product(difference(a(A,B,C),one),D) = difference(a(A,B,C),D),
inference(copy,[status(thm)],[c_6380]) ).
cnf(c_6381,plain,
a(A,B,C) = a(B,C,difference(A,one)),
inference(paramod,[status(thm)],[c_58,c_48]) ).
cnf(c_278,plain,
a(A,B,difference(C,one)) = a(C,A,B),
inference(copy,[status(thm)],[c_6381]) ).
cnf(c_6382,plain,
a(A,B,C) = a(B,C,quotient(one,A)),
inference(paramod,[status(thm)],[c_59,c_53]) ).
cnf(c_285,plain,
a(A,B,quotient(one,C)) = a(C,A,B),
inference(copy,[status(thm)],[c_6382]) ).
cnf(c_6383,plain,
a(A,quotient(one,B),C) = a(C,difference(A,one),B),
inference(paramod,[status(thm)],[c_278,c_48]) ).
cnf(c_446,plain,
a(A,quotient(one,B),C) = a(C,quotient(one,A),B),
inference(paramod,[status(thm)],[c_44,c_6383]) ).
cnf(c_6384,plain,
difference(product(A,B),A) = quotient(difference(B,product(one,A)),A),
inference(paramod,[status(thm)],[c_1,c_66]) ).
cnf(c_640,plain,
difference(product(A,B),A) = quotient(difference(B,A),A),
inference(paramod,[status(thm)],[c_2,c_6384]) ).
cnf(c_6385,plain,
difference(difference(a(A,B,C),one),product(a(A,B,C),product(quotient(one,a(A,B,C)),D))) = quotient(product(a(A,B,C),product(D,difference(a(A,B,C),one))),difference(a(A,B,C),one)),
inference(paramod,[status(thm)],[c_40,c_71]) ).
cnf(c_1291,plain,
difference(difference(a(A,B,C),one),product(a(A,B,C),product(quotient(one,a(A,B,C)),D))) = product(a(A,B,C),D),
inference(paramod,[status(thm)],[c_172,c_6385]) ).
cnf(c_6386,plain,
difference(difference(a(A,B,C),one),one) = product(a(A,B,C),product(quotient(one,a(A,B,C)),a(A,B,C))),
inference(paramod,[status(thm)],[c_72,c_40]) ).
cnf(c_6387,plain,
difference(difference(a(A,B,C),one),one) = product(a(A,B,C),one),
inference(paramod,[status(thm)],[c_6,c_6386]) ).
cnf(c_1390,plain,
difference(difference(a(A,B,C),one),one) = a(A,B,C),
inference(paramod,[status(thm)],[c_1,c_6387]) ).
cnf(c_6388,plain,
product(difference(difference(a(A,B,C),one),one),difference(a(A,B,C),D)) = product(a(A,B,C),product(quotient(one,a(A,B,C)),D)),
inference(paramod,[status(thm)],[c_40,c_73]) ).
cnf(c_6389,plain,
product(a(A,B,C),difference(a(A,B,C),D)) = product(a(A,B,C),product(quotient(one,a(A,B,C)),D)),
inference(paramod,[status(thm)],[c_1390,c_6388]) ).
cnf(c_6390,plain,
D = product(a(A,B,C),product(quotient(one,a(A,B,C)),D)),
inference(paramod,[status(thm)],[c_3,c_6389]) ).
cnf(c_1530,plain,
product(a(A,B,C),product(quotient(one,a(A,B,C)),D)) = D,
inference(copy,[status(thm)],[c_6390]) ).
cnf(c_1559,plain,
difference(difference(a(A,B,C),one),D) = product(a(A,B,C),D),
inference(paramod,[status(thm)],[c_1530,c_1291]) ).
cnf(c_2773,plain,
product(A,difference(a(B,C,A),one)) = product(a(A,B,C),A),
inference(paramod,[status(thm)],[c_196,c_3]) ).
cnf(c_6391,plain,
product(difference(a(A,B,C),one),difference(a(A,B,C),quotient(one,difference(a(A,B,C),one)))) = quotient(one,quotient(one,difference(a(A,B,C),one))),
inference(paramod,[status(thm)],[c_197,c_81]) ).
cnf(c_6392,plain,
product(difference(a(A,B,C),one),difference(a(A,B,C),a(A,B,C))) = quotient(one,quotient(one,difference(a(A,B,C),one))),
inference(paramod,[status(thm)],[c_58,c_6391]) ).
cnf(c_6393,plain,
product(difference(a(A,B,C),one),one) = quotient(one,quotient(one,difference(a(A,B,C),one))),
inference(paramod,[status(thm)],[c_55,c_6392]) ).
cnf(c_6394,plain,
difference(a(A,B,C),one) = quotient(one,quotient(one,difference(a(A,B,C),one))),
inference(paramod,[status(thm)],[c_1,c_6393]) ).
cnf(c_2829,plain,
difference(a(A,B,C),one) = quotient(one,a(A,B,C)),
inference(paramod,[status(thm)],[c_58,c_6394]) ).
cnf(c_2879,plain,
product(A,quotient(one,a(B,C,A))) = product(a(A,B,C),A),
inference(paramod,[status(thm)],[c_2829,c_2773]) ).
cnf(c_2881,plain,
difference(quotient(one,a(A,B,C)),D) = product(a(A,B,C),D),
inference(paramod,[status(thm)],[c_2829,c_1559]) ).
cnf(c_6395,plain,
difference(product(a(A,B,C),A),A) = quotient(difference(quotient(one,a(B,C,A)),A),A),
inference(paramod,[status(thm)],[c_2879,c_640]) ).
cnf(c_6396,plain,
difference(product(a(A,B,C),A),A) = quotient(product(a(B,C,A),A),A),
inference(paramod,[status(thm)],[c_2881,c_6395]) ).
cnf(c_6172,plain,
difference(product(a(A,B,C),A),A) = a(B,C,A),
inference(paramod,[status(thm)],[c_5,c_6396]) ).
cnf(c_6397,plain,
difference(product(a(A,B,C),difference(C,one)),difference(C,one)) = a(A,B,difference(C,one)),
inference(paramod,[status(thm)],[c_53,c_6172]) ).
cnf(c_6219,plain,
difference(product(a(A,B,C),difference(C,one)),difference(C,one)) = a(C,A,B),
inference(paramod,[status(thm)],[c_278,c_6397]) ).
cnf(c_6220,plain,
quotient(A,a(B,C,A)) = product(a(A,B,C),A),
inference(paramod,[status(thm)],[c_6172,c_58]) ).
cnf(c_6398,plain,
quotient(difference(A,one),a(B,C,difference(A,one))) = product(a(B,C,A),difference(A,one)),
inference(paramod,[status(thm)],[c_53,c_6220]) ).
cnf(c_6308,plain,
quotient(difference(A,one),a(A,B,C)) = product(a(B,C,A),difference(A,one)),
inference(paramod,[status(thm)],[c_278,c_6398]) ).
cnf(c_6399,plain,
quotient(difference(A,one),a(A,B,quotient(one,C))) = product(a(C,quotient(one,A),B),difference(A,one)),
inference(paramod,[status(thm)],[c_446,c_6308]) ).
cnf(c_6400,plain,
quotient(difference(A,one),a(C,A,B)) = product(a(C,quotient(one,A),B),difference(A,one)),
inference(paramod,[status(thm)],[c_285,c_6399]) ).
cnf(c_6333,plain,
product(a(A,quotient(one,B),C),difference(B,one)) = quotient(difference(B,one),a(A,B,C)),
inference(copy,[status(thm)],[c_6400]) ).
cnf(c_6401,plain,
product(a(A,difference(B,one),B),difference(B,one)) = product(a(difference(B,one),B,A),difference(B,one)),
inference(paramod,[status(thm)],[c_6308,c_6220]) ).
cnf(c_6402,plain,
product(a(A,quotient(one,B),B),difference(B,one)) = product(a(difference(B,one),B,A),difference(B,one)),
inference(paramod,[status(thm)],[c_44,c_6401]) ).
cnf(c_6403,plain,
quotient(difference(B,one),a(A,B,B)) = product(a(difference(B,one),B,A),difference(B,one)),
inference(paramod,[status(thm)],[c_6333,c_6402]) ).
cnf(c_6353,plain,
quotient(difference(A,one),a(B,A,A)) = product(a(A,B,A),difference(A,one)),
inference(paramod,[status(thm)],[c_53,c_6403]) ).
cnf(c_6404,plain,
difference(product(a(A,B,A),difference(A,one)),difference(A,one)) = a(B,A,A),
inference(paramod,[status(thm)],[c_6353,c_59]) ).
cnf(c_6405,plain,
a(A,A,B) = a(B,A,A),
inference(paramod,[status(thm)],[c_6219,c_6404]) ).
cnf(c_6358,plain,
a(A,B,B) = a(B,B,A),
inference(copy,[status(thm)],[c_6405]) ).
cnf(c_6406,plain,
a(x0,x1,x1) != a(x1,x1,x0),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_6359,plain,
$false,
inference(resolve,[status(thm)],[c_6358,c_6406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.42 % Computer : n017.cluster.edu
% 0.12/5.42 % Model : x86_64 x86_64
% 0.12/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.42 % Memory : 8046.5625MB
% 0.12/5.42 % OS : Linux 6.8.0-71-generic
% 0.12/5.42 % CPULimit : 300
% 0.12/5.42 % WCLimit : 300
% 0.12/5.42 % DateTime : Fri Sep 25 15:41:24 UTC 2026
% 0.12/5.42 % CPUTime :
% 0.12/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.43 % Process 2673752 was started by sandbox on n017,
% 0.12/5.43 % Fri Sep 25 15:41:24 2026
% 0.12/5.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/5.43
% 0.12/5.43 % From the command line: assign(max_seconds, 300).
% 16.44/7.82
% 16.44/7.82 % SZS status Unsatisfiable for theBenchmark
% 16.44/7.82
% 16.44/7.82 % Proof 1 at 1.67 (+ 0.52) seconds.
% 16.44/7.82 % Length of proof is 63.
% 16.44/7.82 % Level of proof is 15.
% 16.44/7.82 % Maximum clause weight is 67.000.
% 16.44/7.82 % Given clauses 306.
% 16.44/7.82
% 16.44/7.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------