%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP777+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 : 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 : Sun Sep 27 07:31:26 AM UTC 2026
% Result : Theorem 0.95s 0.60s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 10
% Syntax : Number of formulae : 146 ( 146 unt; 0 def)
% Number of atoms : 146 ( 145 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 195 ( 0 sgn 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos01,axiom,
! [B,A] : difference(A,product(A,B)) = B,
file('theBenchmark.p',sos01) ).
fof(sos02,axiom,
! [B,A] : product(A,difference(A,B)) = B,
file('theBenchmark.p',sos02) ).
fof(sos03,axiom,
! [B,A] : quotient(product(A,B),B) = A,
file('theBenchmark.p',sos03) ).
fof(sos04,axiom,
! [B,A] : product(quotient(A,B),B) = A,
file('theBenchmark.p',sos04) ).
fof(sos05,axiom,
! [D,C,B,A] : product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)),
file('theBenchmark.p',sos05) ).
fof(sos06,axiom,
! [A] : product(A,A) = A,
file('theBenchmark.p',sos06) ).
fof(sos07,axiom,
! [B,A] : product(product(product(A,B),B),product(B,product(B,A))) = B,
file('theBenchmark.p',sos07) ).
fof(sos08,axiom,
! [C,B,A] : bigC(A,B,C) = product(product(A,B),product(C,A)),
file('theBenchmark.p',sos08) ).
fof(goals,conjecture,
! [X0] : bigC(a,b,X0) = bigC(c,c,X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : bigC(a,b,X0) = bigC(c,c,X0),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_10,plain,
difference(A,product(A,B)) = B,
inference(clausify,[status(thm)],[sos01]) ).
cnf(c_11,plain,
product(A,difference(A,B)) = B,
inference(clausify,[status(thm)],[sos02]) ).
cnf(c_12,plain,
quotient(product(A,B),B) = A,
inference(clausify,[status(thm)],[sos03]) ).
cnf(c_13,plain,
product(quotient(A,B),B) = A,
inference(clausify,[status(thm)],[sos04]) ).
cnf(c_14,plain,
product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)),
inference(clausify,[status(thm)],[sos05]) ).
cnf(c_15,plain,
product(A,A) = A,
inference(clausify,[status(thm)],[sos06]) ).
cnf(c_16,plain,
product(product(product(A,B),B),product(B,product(B,A))) = B,
inference(clausify,[status(thm)],[sos07]) ).
cnf(c_17,plain,
bigC(A,B,C) = product(product(A,B),product(C,A)),
inference(clausify,[status(thm)],[sos08]) ).
fof(sos09,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('theBenchmark.p',sos09) ).
cnf(c_18,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(clausify,[status(thm)],[sos09]) ).
fof(nnf_9,plain,
? [X0] : bigC(c,c,X0) != bigC(a,b,X0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
bigC(c,c,sK0) != bigC(a,b,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_9]) ).
cnf(c_19,negated_conjecture,
bigC(c,c,sK0) != bigC(a,b,sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_1453,negated_conjecture,
product(product(c,c),product(sK0,c)) != bigC(a,b,sK0),
inference(paramod,[status(thm)],[c_17,c_19]) ).
cnf(c_1454,negated_conjecture,
product(c,product(sK0,c)) != bigC(a,b,sK0),
inference(paramod,[status(thm)],[c_15,c_1453]) ).
cnf(c_1455,negated_conjecture,
product(c,product(sK0,c)) != product(product(a,b),product(sK0,a)),
inference(paramod,[status(thm)],[c_17,c_1454]) ).
cnf(c_20,negated_conjecture,
product(product(a,b),product(sK0,a)) != product(c,product(sK0,c)),
inference(copy,[status(thm)],[c_1455]) ).
cnf(c_21,plain,
quotient(A,difference(B,A)) = B,
inference(paramod,[status(thm)],[c_11,c_12]) ).
cnf(c_22,plain,
difference(quotient(A,B),A) = B,
inference(paramod,[status(thm)],[c_13,c_10]) ).
cnf(c_1456,plain,
product(product(A,B),C) = product(product(A,D),product(B,difference(D,C))),
inference(paramod,[status(thm)],[c_11,c_14]) ).
cnf(c_25,plain,
product(product(A,B),product(C,difference(B,D))) = product(product(A,C),D),
inference(copy,[status(thm)],[c_1456]) ).
cnf(c_26,plain,
quotient(product(product(A,B),product(C,D)),product(B,D)) = product(A,C),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_1457,plain,
product(product(A,B),C) = product(product(A,quotient(C,D)),product(B,D)),
inference(paramod,[status(thm)],[c_13,c_14]) ).
cnf(c_28,plain,
product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B),
inference(copy,[status(thm)],[c_1457]) ).
cnf(c_1458,plain,
product(A,product(B,C)) = product(product(A,B),product(A,C)),
inference(paramod,[status(thm)],[c_15,c_14]) ).
cnf(c_33,plain,
product(product(A,B),product(A,C)) = product(A,product(B,C)),
inference(copy,[status(thm)],[c_1458]) ).
cnf(c_1459,plain,
product(product(A,B),C) = product(product(A,C),product(B,C)),
inference(paramod,[status(thm)],[c_15,c_14]) ).
cnf(c_34,plain,
product(product(A,B),product(C,B)) = product(product(A,C),B),
inference(copy,[status(thm)],[c_1459]) ).
cnf(c_37,plain,
product(product(product(difference(A,B),A),A),product(A,B)) = A,
inference(paramod,[status(thm)],[c_11,c_16]) ).
cnf(c_47,plain,
difference(product(a,c),product(a,b)) = product(c,b),
inference(paramod,[status(thm)],[c_18,c_10]) ).
cnf(c_57,plain,
quotient(product(A,product(B,C)),product(A,C)) = product(A,B),
inference(paramod,[status(thm)],[c_33,c_12]) ).
cnf(c_64,plain,
product(product(A,B),A) = product(A,product(B,A)),
inference(paramod,[status(thm)],[c_15,c_33]) ).
cnf(c_75,plain,
quotient(product(A,product(B,A)),A) = product(A,B),
inference(paramod,[status(thm)],[c_64,c_12]) ).
cnf(c_84,plain,
quotient(product(A,B),A) = product(A,quotient(B,A)),
inference(paramod,[status(thm)],[c_13,c_75]) ).
cnf(c_1460,plain,
quotient(product(product(c,b),product(a,b)),product(c,b)) = product(product(c,b),product(a,c)),
inference(paramod,[status(thm)],[c_18,c_75]) ).
cnf(c_87,plain,
quotient(product(product(c,a),b),product(c,b)) = product(product(c,b),product(a,c)),
inference(paramod,[status(thm)],[c_34,c_1460]) ).
cnf(c_1461,plain,
quotient(A,B) = product(B,quotient(difference(B,A),B)),
inference(paramod,[status(thm)],[c_11,c_84]) ).
cnf(c_89,plain,
product(A,quotient(difference(A,B),A)) = quotient(B,A),
inference(copy,[status(thm)],[c_1461]) ).
cnf(c_1462,plain,
difference(A,quotient(B,A)) = quotient(difference(A,B),A),
inference(paramod,[status(thm)],[c_89,c_10]) ).
cnf(c_97,plain,
quotient(difference(A,B),A) = difference(A,quotient(B,A)),
inference(copy,[status(thm)],[c_1462]) ).
cnf(c_98,plain,
product(difference(A,quotient(B,A)),A) = difference(A,B),
inference(paramod,[status(thm)],[c_97,c_13]) ).
cnf(c_1463,plain,
product(difference(A,B),A) = difference(A,product(B,A)),
inference(paramod,[status(thm)],[c_12,c_98]) ).
cnf(c_126,plain,
difference(A,product(B,A)) = product(difference(A,B),A),
inference(copy,[status(thm)],[c_1463]) ).
cnf(c_142,plain,
quotient(product(A,B),product(difference(B,A),B)) = B,
inference(paramod,[status(thm)],[c_126,c_21]) ).
cnf(c_1464,plain,
difference(product(a,c),product(product(a,b),product(a,c))) = product(product(c,b),product(a,c)),
inference(paramod,[status(thm)],[c_47,c_126]) ).
cnf(c_143,plain,
difference(product(a,c),product(a,product(b,c))) = product(product(c,b),product(a,c)),
inference(paramod,[status(thm)],[c_33,c_1464]) ).
cnf(c_149,plain,
quotient(product(A,quotient(A,B)),product(B,quotient(A,B))) = quotient(A,B),
inference(paramod,[status(thm)],[c_22,c_142]) ).
cnf(c_155,plain,
quotient(product(product(A,B),B),product(product(difference(B,A),B),B)) = B,
inference(paramod,[status(thm)],[c_126,c_142]) ).
cnf(c_167,plain,
quotient(product(A,B),product(A,C)) = product(A,quotient(B,C)),
inference(paramod,[status(thm)],[c_13,c_57]) ).
cnf(c_1465,plain,
quotient(A,product(B,C)) = product(B,quotient(difference(B,A),C)),
inference(paramod,[status(thm)],[c_11,c_167]) ).
cnf(c_223,plain,
product(A,quotient(difference(A,B),C)) = quotient(B,product(A,C)),
inference(copy,[status(thm)],[c_1465]) ).
cnf(c_1466,plain,
quotient(product(A,B),C) = product(A,quotient(B,difference(A,C))),
inference(paramod,[status(thm)],[c_11,c_167]) ).
cnf(c_224,plain,
product(A,quotient(B,difference(A,C))) = quotient(product(A,B),C),
inference(copy,[status(thm)],[c_1466]) ).
cnf(c_229,plain,
quotient(A,product(A,B)) = product(A,quotient(A,B)),
inference(paramod,[status(thm)],[c_15,c_167]) ).
cnf(c_234,plain,
difference(product(A,quotient(B,C)),product(A,B)) = product(A,C),
inference(paramod,[status(thm)],[c_167,c_22]) ).
cnf(c_251,plain,
difference(product(A,quotient(A,B)),A) = product(A,B),
inference(paramod,[status(thm)],[c_229,c_22]) ).
cnf(c_260,plain,
difference(product(A,B),A) = product(A,difference(B,A)),
inference(paramod,[status(thm)],[c_21,c_251]) ).
cnf(c_278,plain,
difference(A,quotient(B,product(A,C))) = quotient(difference(A,B),C),
inference(paramod,[status(thm)],[c_223,c_10]) ).
cnf(c_287,plain,
product(product(A,B),quotient(C,product(A,D))) = product(A,product(B,quotient(difference(A,C),D))),
inference(paramod,[status(thm)],[c_223,c_33]) ).
cnf(c_337,plain,
quotient(product(A,product(B,C)),product(D,C)) = product(quotient(A,D),B),
inference(paramod,[status(thm)],[c_13,c_26]) ).
cnf(c_338,plain,
quotient(product(product(A,B),C),product(B,D)) = product(A,quotient(C,D)),
inference(paramod,[status(thm)],[c_13,c_26]) ).
cnf(c_348,plain,
difference(product(A,B),product(A,C)) = product(A,difference(B,C)),
inference(paramod,[status(thm)],[c_21,c_234]) ).
cnf(c_1467,plain,
product(a,difference(c,product(b,c))) = product(product(c,b),product(a,c)),
inference(paramod,[status(thm)],[c_348,c_143]) ).
cnf(c_1468,plain,
product(a,product(difference(c,b),c)) = product(product(c,b),product(a,c)),
inference(paramod,[status(thm)],[c_126,c_1467]) ).
cnf(c_364,plain,
product(product(c,b),product(a,c)) = product(a,product(difference(c,b),c)),
inference(copy,[status(thm)],[c_1468]) ).
cnf(c_365,plain,
product(a,difference(c,b)) = product(c,b),
inference(paramod,[status(thm)],[c_348,c_47]) ).
cnf(c_367,plain,
quotient(product(product(c,a),b),product(c,b)) = product(a,product(difference(c,b),c)),
inference(paramod,[status(thm)],[c_364,c_87]) ).
cnf(c_383,plain,
product(product(A,c),product(c,b)) = product(product(A,a),b),
inference(paramod,[status(thm)],[c_365,c_25]) ).
cnf(c_1469,plain,
product(product(A,B),quotient(C,product(A,difference(B,D)))) = quotient(product(product(A,B),C),product(A,D)),
inference(paramod,[status(thm)],[c_348,c_224]) ).
cnf(c_1470,plain,
product(A,product(B,quotient(difference(A,C),difference(B,D)))) = quotient(product(product(A,B),C),product(A,D)),
inference(paramod,[status(thm)],[c_287,c_1469]) ).
cnf(c_1471,plain,
product(A,quotient(product(B,difference(A,C)),D)) = quotient(product(product(A,B),C),product(A,D)),
inference(paramod,[status(thm)],[c_224,c_1470]) ).
cnf(c_411,plain,
quotient(product(product(A,B),C),product(A,D)) = product(A,quotient(product(B,difference(A,C)),D)),
inference(copy,[status(thm)],[c_1471]) ).
cnf(c_1472,plain,
product(c,quotient(product(a,difference(c,b)),b)) = product(a,product(difference(c,b),c)),
inference(paramod,[status(thm)],[c_411,c_367]) ).
cnf(c_1473,plain,
product(c,quotient(product(c,b),b)) = product(a,product(difference(c,b),c)),
inference(paramod,[status(thm)],[c_365,c_1472]) ).
cnf(c_1474,plain,
product(c,c) = product(a,product(difference(c,b),c)),
inference(paramod,[status(thm)],[c_12,c_1473]) ).
cnf(c_1475,plain,
c = product(a,product(difference(c,b),c)),
inference(paramod,[status(thm)],[c_15,c_1474]) ).
cnf(c_423,plain,
product(a,product(difference(c,b),c)) = c,
inference(copy,[status(thm)],[c_1475]) ).
cnf(c_1476,plain,
difference(A,quotient(B,C)) = quotient(difference(A,B),difference(A,C)),
inference(paramod,[status(thm)],[c_11,c_278]) ).
cnf(c_433,plain,
quotient(difference(A,B),difference(A,C)) = difference(A,quotient(B,C)),
inference(copy,[status(thm)],[c_1476]) ).
cnf(c_459,plain,
product(product(A,quotient(B,C)),C) = product(product(A,C),B),
inference(paramod,[status(thm)],[c_15,c_28]) ).
cnf(c_489,plain,
product(difference(A,quotient(B,C)),difference(A,C)) = difference(A,B),
inference(paramod,[status(thm)],[c_433,c_13]) ).
cnf(c_625,plain,
product(difference(A,B),difference(A,C)) = difference(A,product(B,C)),
inference(paramod,[status(thm)],[c_12,c_489]) ).
cnf(c_1477,plain,
difference(a,c) = product(difference(c,b),c),
inference(paramod,[status(thm)],[c_423,c_10]) ).
cnf(c_703,plain,
product(difference(c,b),c) = difference(a,c),
inference(copy,[status(thm)],[c_1477]) ).
cnf(c_706,plain,
quotient(difference(a,c),c) = difference(c,b),
inference(paramod,[status(thm)],[c_703,c_12]) ).
cnf(c_1478,plain,
product(a,difference(c,b)) = quotient(c,product(a,c)),
inference(paramod,[status(thm)],[c_706,c_223]) ).
cnf(c_1479,plain,
product(c,b) = quotient(c,product(a,c)),
inference(paramod,[status(thm)],[c_365,c_1478]) ).
cnf(c_732,plain,
quotient(c,product(a,c)) = product(c,b),
inference(copy,[status(thm)],[c_1479]) ).
cnf(c_1480,plain,
difference(product(c,b),c) = product(a,c),
inference(paramod,[status(thm)],[c_732,c_22]) ).
cnf(c_813,plain,
product(c,difference(b,c)) = product(a,c),
inference(paramod,[status(thm)],[c_260,c_1480]) ).
cnf(c_1481,plain,
quotient(product(c,product(c,b)),product(product(a,c),quotient(c,product(a,c)))) = quotient(c,product(a,c)),
inference(paramod,[status(thm)],[c_732,c_149]) ).
cnf(c_1482,plain,
quotient(product(c,product(c,b)),product(product(a,c),product(c,b))) = quotient(c,product(a,c)),
inference(paramod,[status(thm)],[c_732,c_1481]) ).
cnf(c_1483,plain,
quotient(product(c,product(c,b)),product(product(a,a),b)) = quotient(c,product(a,c)),
inference(paramod,[status(thm)],[c_383,c_1482]) ).
cnf(c_1484,plain,
quotient(product(c,product(c,b)),product(a,b)) = quotient(c,product(a,c)),
inference(paramod,[status(thm)],[c_15,c_1483]) ).
cnf(c_1485,plain,
product(quotient(c,a),c) = quotient(c,product(a,c)),
inference(paramod,[status(thm)],[c_337,c_1484]) ).
cnf(c_814,plain,
product(quotient(c,a),c) = product(c,b),
inference(paramod,[status(thm)],[c_732,c_1485]) ).
cnf(c_1486,plain,
difference(c,product(a,c)) = difference(b,c),
inference(paramod,[status(thm)],[c_813,c_10]) ).
cnf(c_818,plain,
product(difference(c,a),c) = difference(b,c),
inference(paramod,[status(thm)],[c_126,c_1486]) ).
cnf(c_1487,plain,
quotient(product(c,b),c) = quotient(c,a),
inference(paramod,[status(thm)],[c_814,c_12]) ).
cnf(c_845,plain,
product(c,quotient(b,c)) = quotient(c,a),
inference(paramod,[status(thm)],[c_84,c_1487]) ).
cnf(c_1488,plain,
quotient(product(c,b),quotient(c,a)) = product(quotient(c,a),quotient(c,quotient(c,a))),
inference(paramod,[status(thm)],[c_814,c_84]) ).
cnf(c_852,plain,
product(quotient(c,a),quotient(c,quotient(c,a))) = quotient(product(c,b),quotient(c,a)),
inference(copy,[status(thm)],[c_1488]) ).
cnf(c_954,plain,
difference(c,quotient(c,a)) = quotient(b,c),
inference(paramod,[status(thm)],[c_845,c_10]) ).
cnf(c_969,plain,
quotient(product(c,A),quotient(c,a)) = product(c,quotient(A,quotient(b,c))),
inference(paramod,[status(thm)],[c_845,c_167]) ).
cnf(c_989,plain,
product(quotient(c,a),quotient(c,quotient(c,a))) = product(c,quotient(b,quotient(b,c))),
inference(paramod,[status(thm)],[c_969,c_852]) ).
cnf(c_1489,plain,
product(difference(c,A),quotient(b,c)) = difference(c,product(A,quotient(c,a))),
inference(paramod,[status(thm)],[c_954,c_625]) ).
cnf(c_1046,plain,
difference(c,product(A,quotient(c,a))) = product(difference(c,A),quotient(b,c)),
inference(copy,[status(thm)],[c_1489]) ).
cnf(c_1490,plain,
quotient(A,product(A,B)) = product(product(difference(A,B),A),A),
inference(paramod,[status(thm)],[c_37,c_12]) ).
cnf(c_1491,plain,
product(A,quotient(A,B)) = product(product(difference(A,B),A),A),
inference(paramod,[status(thm)],[c_229,c_1490]) ).
cnf(c_1129,plain,
product(product(difference(A,B),A),A) = product(A,quotient(A,B)),
inference(copy,[status(thm)],[c_1491]) ).
cnf(c_1492,plain,
product(product(product(difference(c,quotient(b,c)),c),c),quotient(c,a)) = c,
inference(paramod,[status(thm)],[c_845,c_37]) ).
cnf(c_1493,plain,
product(product(difference(c,b),c),quotient(c,a)) = c,
inference(paramod,[status(thm)],[c_98,c_1492]) ).
cnf(c_1155,plain,
product(difference(a,c),quotient(c,a)) = c,
inference(paramod,[status(thm)],[c_703,c_1493]) ).
cnf(c_1494,plain,
quotient(product(product(A,B),B),product(B,quotient(B,A))) = B,
inference(paramod,[status(thm)],[c_1129,c_155]) ).
cnf(c_1161,plain,
product(A,quotient(B,quotient(B,A))) = B,
inference(paramod,[status(thm)],[c_338,c_1494]) ).
cnf(c_1163,plain,
product(quotient(c,a),quotient(c,quotient(c,a))) = b,
inference(paramod,[status(thm)],[c_1161,c_989]) ).
cnf(c_1165,plain,
quotient(c,quotient(c,a)) = difference(a,c),
inference(paramod,[status(thm)],[c_1155,c_12]) ).
cnf(c_1195,plain,
product(quotient(c,a),difference(a,c)) = b,
inference(paramod,[status(thm)],[c_1165,c_1163]) ).
cnf(c_1202,plain,
quotient(b,difference(a,c)) = quotient(c,a),
inference(paramod,[status(thm)],[c_1195,c_12]) ).
cnf(c_1495,plain,
product(b,quotient(c,a)) = product(quotient(c,a),product(difference(a,c),quotient(c,a))),
inference(paramod,[status(thm)],[c_1195,c_64]) ).
cnf(c_1496,plain,
product(b,quotient(c,a)) = product(quotient(c,a),c),
inference(paramod,[status(thm)],[c_1155,c_1495]) ).
cnf(c_1208,plain,
product(b,quotient(c,a)) = product(c,b),
inference(paramod,[status(thm)],[c_814,c_1496]) ).
cnf(c_1497,plain,
product(a,quotient(c,a)) = quotient(product(a,b),c),
inference(paramod,[status(thm)],[c_1202,c_224]) ).
cnf(c_1234,plain,
quotient(product(a,b),c) = product(a,quotient(c,a)),
inference(copy,[status(thm)],[c_1497]) ).
cnf(c_1498,plain,
difference(b,product(c,b)) = quotient(c,a),
inference(paramod,[status(thm)],[c_1208,c_10]) ).
cnf(c_1235,plain,
product(difference(b,c),b) = quotient(c,a),
inference(paramod,[status(thm)],[c_126,c_1498]) ).
cnf(c_1499,plain,
product(difference(c,product(a,quotient(c,a))),c) = difference(c,product(a,b)),
inference(paramod,[status(thm)],[c_1234,c_98]) ).
cnf(c_1500,plain,
product(product(difference(c,a),quotient(b,c)),c) = difference(c,product(a,b)),
inference(paramod,[status(thm)],[c_1046,c_1499]) ).
cnf(c_1501,plain,
product(product(difference(c,a),c),b) = difference(c,product(a,b)),
inference(paramod,[status(thm)],[c_459,c_1500]) ).
cnf(c_1502,plain,
product(difference(b,c),b) = difference(c,product(a,b)),
inference(paramod,[status(thm)],[c_818,c_1501]) ).
cnf(c_1503,plain,
quotient(c,a) = difference(c,product(a,b)),
inference(paramod,[status(thm)],[c_1235,c_1502]) ).
cnf(c_1403,plain,
difference(c,product(a,b)) = quotient(c,a),
inference(copy,[status(thm)],[c_1503]) ).
cnf(c_1405,plain,
product(c,quotient(c,a)) = product(a,b),
inference(paramod,[status(thm)],[c_1403,c_11]) ).
cnf(c_1504,plain,
product(product(a,b),product(A,a)) = product(product(c,A),c),
inference(paramod,[status(thm)],[c_1405,c_28]) ).
cnf(c_1451,plain,
product(product(a,b),product(A,a)) = product(c,product(A,c)),
inference(paramod,[status(thm)],[c_64,c_1504]) ).
cnf(c_1452,plain,
$false,
inference(resolve,[status(thm)],[c_1451,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 15:46:20 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.35 % Process 2481930 was started by sandbox on n012,
% 0.12/0.35 % Fri Sep 25 15:46:20 2026
% 0.12/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.95/0.60
% 0.95/0.60 % SZS status Theorem for theBenchmark
% 0.95/0.60
% 0.95/0.60 % Proof 1 at 0.18 (+ 0.05) seconds.
% 0.95/0.60 % Length of proof is 90.
% 0.95/0.60 % Level of proof is 28.
% 0.95/0.60 % Maximum clause weight is 54.000.
% 0.95/0.60 % Given clauses 95.
% 0.95/0.60
% 0.95/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------