%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG131-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:26:44 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 95
% Number of leaves : 10
% Syntax : Number of formulae : 147 ( 147 unt; 0 def)
% Number of atoms : 147 ( 146 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 95 ( 95 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(plus_comm,axiom,
! [VAR_0,VAR_1] : plus(VAR_0,VAR_1) = plus(VAR_1,VAR_0),
file('theBenchmark.p',plus_comm) ).
cnf(c_1,plain,
plus(A,B) = plus(B,A),
inference(clausify,[status(thm)],[plus_comm]) ).
fof(plus_assoc,axiom,
! [VAR_0,VAR_1,VAR_2] : plus(VAR_0,plus(VAR_1,VAR_2)) = plus(plus(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',plus_assoc) ).
cnf(c_2,plain,
plus(A,plus(B,C)) = plus(plus(A,B),C),
inference(clausify,[status(thm)],[plus_assoc]) ).
cnf(c_3,plain,
plus(plus(A,B),C) = plus(A,plus(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(plus_zero,axiom,
! [VAR_0] : plus(zero,VAR_0) = VAR_0,
file('theBenchmark.p',plus_zero) ).
cnf(c_4,plain,
plus(zero,A) = A,
inference(clausify,[status(thm)],[plus_zero]) ).
fof(plus_inv,axiom,
! [VAR_0] : plus(VAR_0,minus(VAR_0)) = zero,
file('theBenchmark.p',plus_inv) ).
cnf(c_5,plain,
plus(A,minus(A)) = zero,
inference(clausify,[status(thm)],[plus_inv]) ).
fof(times_assoc,axiom,
! [VAR_0,VAR_1,VAR_2] : times(VAR_0,times(VAR_1,VAR_2)) = times(times(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',times_assoc) ).
cnf(c_6,plain,
times(A,times(B,C)) = times(times(A,B),C),
inference(clausify,[status(thm)],[times_assoc]) ).
cnf(c_7,plain,
times(times(A,B),C) = times(A,times(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(times_com,axiom,
! [VAR_0,VAR_1] : times(VAR_0,VAR_1) = times(VAR_1,VAR_0),
file('theBenchmark.p',times_com) ).
cnf(c_8,plain,
times(A,B) = times(B,A),
inference(clausify,[status(thm)],[times_com]) ).
fof(square,axiom,
! [VAR_0] : sq(VAR_0) = times(VAR_0,VAR_0),
file('theBenchmark.p',square) ).
cnf(c_9,plain,
sq(A) = times(A,A),
inference(clausify,[status(thm)],[square]) ).
fof(distrib1,axiom,
! [VAR_0,VAR_1,VAR_2] : times(VAR_0,plus(VAR_1,VAR_2)) = plus(times(VAR_0,VAR_1),times(VAR_0,VAR_2)),
file('theBenchmark.p',distrib1) ).
cnf(c_10,plain,
times(A,plus(B,C)) = plus(times(A,B),times(A,C)),
inference(clausify,[status(thm)],[distrib1]) ).
fof(distrib2,axiom,
! [VAR_0,VAR_1,VAR_2] : times(plus(VAR_0,VAR_1),VAR_2) = plus(times(VAR_0,VAR_2),times(VAR_1,VAR_2)),
file('theBenchmark.p',distrib2) ).
cnf(c_11,plain,
times(plus(A,B),C) = plus(times(A,C),times(B,C)),
inference(clausify,[status(thm)],[distrib2]) ).
fof(goals,axiom,
times(plus(sq(a),sq(b)),plus(sq(c),sq(d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
file('theBenchmark.p',goals) ).
cnf(c_12,plain,
times(plus(sq(a),sq(b)),plus(sq(c),sq(d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_105,plain,
times(plus(times(a,a),sq(b)),plus(sq(c),sq(d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_9,c_12]) ).
cnf(c_106,plain,
times(plus(times(a,a),times(b,b)),plus(sq(c),sq(d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_9,c_105]) ).
cnf(c_107,plain,
times(plus(times(a,a),times(b,b)),plus(times(c,c),sq(d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_9,c_106]) ).
cnf(c_108,plain,
times(plus(times(a,a),times(b,b)),plus(times(c,c),times(d,d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_9,c_107]) ).
cnf(c_109,plain,
plus(times(plus(times(a,a),times(b,b)),times(c,c)),times(plus(times(a,a),times(b,b)),times(d,d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_10,c_108]) ).
cnf(c_110,plain,
plus(plus(times(times(a,a),times(c,c)),times(times(b,b),times(c,c))),times(plus(times(a,a),times(b,b)),times(d,d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_11,c_109]) ).
cnf(c_111,plain,
plus(plus(times(a,times(a,times(c,c))),times(times(b,b),times(c,c))),times(plus(times(a,a),times(b,b)),times(d,d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_110]) ).
cnf(c_112,plain,
plus(plus(times(a,times(a,times(c,c))),times(b,times(b,times(c,c)))),times(plus(times(a,a),times(b,b)),times(d,d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_111]) ).
cnf(c_113,plain,
plus(plus(times(a,times(a,times(c,c))),times(b,times(b,times(c,c)))),plus(times(times(a,a),times(d,d)),times(times(b,b),times(d,d)))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_11,c_112]) ).
cnf(c_114,plain,
plus(plus(times(a,times(a,times(c,c))),times(b,times(b,times(c,c)))),plus(times(a,times(a,times(d,d))),times(times(b,b),times(d,d)))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_113]) ).
cnf(c_115,plain,
plus(plus(times(a,times(a,times(c,c))),times(b,times(b,times(c,c)))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d))))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_114]) ).
cnf(c_116,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_3,c_115]) ).
cnf(c_117,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(sq(plus(times(a,c),times(d,minus(b)))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_8,c_116]) ).
cnf(c_118,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(times(plus(times(a,c),times(d,minus(b))),plus(times(a,c),times(d,minus(b)))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_9,c_117]) ).
cnf(c_119,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(plus(times(a,c),times(d,minus(b))),times(a,c)),times(plus(times(a,c),times(d,minus(b))),times(d,minus(b)))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_10,c_118]) ).
cnf(c_120,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(times(a,c),plus(times(a,c),times(d,minus(b)))),times(plus(times(a,c),times(d,minus(b))),times(d,minus(b)))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_8,c_119]) ).
cnf(c_121,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(plus(times(times(a,c),times(a,c)),times(times(a,c),times(d,minus(b)))),times(plus(times(a,c),times(d,minus(b))),times(d,minus(b)))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_10,c_120]) ).
cnf(c_122,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(plus(times(a,times(c,times(a,c))),times(times(a,c),times(d,minus(b)))),times(plus(times(a,c),times(d,minus(b))),times(d,minus(b)))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_121]) ).
cnf(c_123,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(plus(times(a,times(c,times(a,c))),times(a,times(c,times(d,minus(b))))),times(plus(times(a,c),times(d,minus(b))),times(d,minus(b)))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_122]) ).
cnf(c_124,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(plus(times(a,times(c,times(a,c))),times(a,times(c,times(d,minus(b))))),times(times(d,minus(b)),plus(times(a,c),times(d,minus(b))))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_8,c_123]) ).
cnf(c_125,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(plus(times(a,times(c,times(a,c))),times(a,times(c,times(d,minus(b))))),plus(times(times(d,minus(b)),times(a,c)),times(times(d,minus(b)),times(d,minus(b))))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_10,c_124]) ).
cnf(c_126,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(plus(times(a,times(c,times(a,c))),times(a,times(c,times(d,minus(b))))),plus(times(times(a,c),times(d,minus(b))),times(times(d,minus(b)),times(d,minus(b))))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_8,c_125]) ).
cnf(c_127,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(plus(times(a,times(c,times(a,c))),times(a,times(c,times(d,minus(b))))),plus(times(a,times(c,times(d,minus(b)))),times(times(d,minus(b)),times(d,minus(b))))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_126]) ).
cnf(c_128,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(plus(times(a,times(c,times(a,c))),times(a,times(c,times(d,minus(b))))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b)))))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_127]) ).
cnf(c_129,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),sq(plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_3,c_128]) ).
cnf(c_130,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),times(plus(times(a,d),times(b,c)),plus(times(a,d),times(b,c)))),
inference(paramod,[status(thm)],[c_9,c_129]) ).
cnf(c_131,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(times(plus(times(a,d),times(b,c)),times(a,d)),times(plus(times(a,d),times(b,c)),times(b,c)))),
inference(paramod,[status(thm)],[c_10,c_130]) ).
cnf(c_132,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(times(times(a,d),plus(times(a,d),times(b,c))),times(plus(times(a,d),times(b,c)),times(b,c)))),
inference(paramod,[status(thm)],[c_8,c_131]) ).
cnf(c_133,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(times(a,d),times(a,d)),times(times(a,d),times(b,c))),times(plus(times(a,d),times(b,c)),times(b,c)))),
inference(paramod,[status(thm)],[c_10,c_132]) ).
cnf(c_134,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(a,times(d,times(a,d))),times(times(a,d),times(b,c))),times(plus(times(a,d),times(b,c)),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_133]) ).
cnf(c_135,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))),times(plus(times(a,d),times(b,c)),times(b,c)))),
inference(paramod,[status(thm)],[c_7,c_134]) ).
cnf(c_136,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))),times(times(b,c),plus(times(a,d),times(b,c))))),
inference(paramod,[status(thm)],[c_8,c_135]) ).
cnf(c_137,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))),plus(times(times(b,c),times(a,d)),times(times(b,c),times(b,c))))),
inference(paramod,[status(thm)],[c_10,c_136]) ).
cnf(c_138,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))),plus(times(times(a,d),times(b,c)),times(times(b,c),times(b,c))))),
inference(paramod,[status(thm)],[c_8,c_137]) ).
cnf(c_139,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))),plus(times(a,times(d,times(b,c))),times(times(b,c),times(b,c))))),
inference(paramod,[status(thm)],[c_7,c_138]) ).
cnf(c_140,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))),plus(times(a,times(d,times(b,c))),times(b,times(c,times(b,c)))))),
inference(paramod,[status(thm)],[c_7,c_139]) ).
cnf(c_141,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))),plus(times(b,times(c,times(b,c))),times(a,times(d,times(b,c)))))),
inference(paramod,[status(thm)],[c_1,c_140]) ).
cnf(c_142,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(plus(times(b,times(c,times(b,c))),times(a,times(d,times(b,c)))),plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))))),
inference(paramod,[status(thm)],[c_1,c_141]) ).
cnf(c_143,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))),plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c))))))),
inference(paramod,[status(thm)],[c_3,c_142]) ).
cnf(c_144,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b)))))))),
inference(paramod,[status(thm)],[c_1,c_143]) ).
cnf(c_145,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(times(b,times(c,times(b,c))),plus(plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c))))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))))),
inference(paramod,[status(thm)],[c_3,c_144]) ).
cnf(c_146,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(plus(times(a,times(d,times(a,d))),times(a,times(d,times(b,c)))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b)))))))))),
inference(paramod,[status(thm)],[c_3,c_145]) ).
cnf(c_147,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))))))),
inference(paramod,[status(thm)],[c_3,c_146]) ).
cnf(c_13,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(copy,[status(thm)],[c_147]) ).
cnf(c_148,plain,
plus(plus(A,B),C) = plus(B,plus(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_15,plain,
plus(A,plus(B,C)) = plus(B,plus(A,C)),
inference(paramod,[status(thm)],[c_3,c_148]) ).
cnf(c_149,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),plus(times(a,times(c,times(a,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_13]) ).
cnf(c_150,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_149]) ).
cnf(c_151,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_150]) ).
cnf(c_152,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(d,times(a,d))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_151]) ).
cnf(c_153,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(a,d))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_152]) ).
cnf(c_154,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_153]) ).
cnf(c_155,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_154]) ).
cnf(c_156,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(b,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_155]) ).
cnf(c_157,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_156]) ).
cnf(c_158,plain,
plus(times(b,times(c,times(b,c))),plus(times(a,times(c,times(a,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_157]) ).
cnf(c_16,plain,
plus(times(a,times(c,times(a,c))),plus(times(b,times(c,times(b,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_158]) ).
cnf(c_159,plain,
A = plus(A,zero),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_17,plain,
plus(A,zero) = A,
inference(copy,[status(thm)],[c_159]) ).
cnf(c_160,plain,
plus(zero,A) = plus(B,plus(minus(B),A)),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_161,plain,
A = plus(B,plus(minus(B),A)),
inference(paramod,[status(thm)],[c_4,c_160]) ).
cnf(c_18,plain,
plus(A,plus(minus(A),B)) = B,
inference(copy,[status(thm)],[c_161]) ).
cnf(c_162,plain,
times(times(A,B),C) = times(B,times(A,C)),
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_21,plain,
times(A,times(B,C)) = times(B,times(A,C)),
inference(paramod,[status(thm)],[c_7,c_162]) ).
cnf(c_163,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(c,times(b,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_16]) ).
cnf(c_164,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(d,times(a,d))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_163]) ).
cnf(c_165,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(a,times(d,d))),plus(times(a,times(d,times(b,c))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_164]) ).
cnf(c_166,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(a,times(d,d))),plus(times(a,times(b,times(d,c))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_165]) ).
cnf(c_167,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(a,times(d,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(d,times(b,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_8,c_166]) ).
cnf(c_168,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(a,times(d,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(d,c))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_167]) ).
cnf(c_169,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(a,times(d,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),times(d,times(minus(b),times(d,minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_8,c_168]) ).
cnf(c_170,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(a,times(d,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_169]) ).
cnf(c_171,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(times(a,times(b,times(c,d))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_170]) ).
cnf(c_172,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_171]) ).
cnf(c_173,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(b,times(c,d))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_172]) ).
cnf(c_174,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(a,times(d,d))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_173]) ).
cnf(c_175,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_174]) ).
cnf(c_176,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_175]) ).
cnf(c_177,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(a,times(d,d))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_176]) ).
cnf(c_22,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(times(a,times(c,times(d,minus(b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_177]) ).
cnf(c_178,plain,
plus(A,zero) = plus(B,plus(A,minus(B))),
inference(paramod,[status(thm)],[c_5,c_15]) ).
cnf(c_179,plain,
A = plus(B,plus(A,minus(B))),
inference(paramod,[status(thm)],[c_17,c_178]) ).
cnf(c_27,plain,
plus(A,plus(B,minus(A))) = B,
inference(copy,[status(thm)],[c_179]) ).
cnf(c_180,plain,
plus(A,zero) = minus(minus(A)),
inference(paramod,[status(thm)],[c_5,c_18]) ).
cnf(c_181,plain,
A = minus(minus(A)),
inference(paramod,[status(thm)],[c_17,c_180]) ).
cnf(c_31,plain,
minus(minus(A)) = A,
inference(copy,[status(thm)],[c_181]) ).
cnf(c_182,plain,
times(A,B) = plus(times(A,C),times(A,plus(minus(C),B))),
inference(paramod,[status(thm)],[c_18,c_10]) ).
cnf(c_183,plain,
times(A,B) = plus(times(A,C),plus(times(A,minus(C)),times(A,B))),
inference(paramod,[status(thm)],[c_10,c_182]) ).
cnf(c_32,plain,
plus(times(A,B),plus(times(A,minus(B)),times(A,C))) = times(A,C),
inference(copy,[status(thm)],[c_183]) ).
cnf(c_184,plain,
plus(A,B) = plus(C,plus(A,plus(minus(C),B))),
inference(paramod,[status(thm)],[c_18,c_15]) ).
cnf(c_34,plain,
plus(A,plus(B,plus(minus(A),C))) = plus(B,C),
inference(copy,[status(thm)],[c_184]) ).
cnf(c_46,plain,
plus(minus(A),plus(B,A)) = B,
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_185,plain,
plus(minus(plus(A,B)),A) = minus(B),
inference(paramod,[status(thm)],[c_46,c_46]) ).
cnf(c_54,plain,
plus(A,minus(plus(A,B))) = minus(B),
inference(paramod,[status(thm)],[c_1,c_185]) ).
cnf(c_186,plain,
plus(minus(A),minus(B)) = minus(plus(B,A)),
inference(paramod,[status(thm)],[c_46,c_54]) ).
cnf(c_71,plain,
minus(plus(A,B)) = plus(minus(B),minus(A)),
inference(copy,[status(thm)],[c_186]) ).
cnf(c_187,plain,
plus(minus(plus(times(A,minus(B)),times(A,C))),times(A,C)) = times(A,B),
inference(paramod,[status(thm)],[c_32,c_46]) ).
cnf(c_188,plain,
plus(plus(minus(times(A,C)),minus(times(A,minus(B)))),times(A,C)) = times(A,B),
inference(paramod,[status(thm)],[c_71,c_187]) ).
cnf(c_189,plain,
plus(times(A,C),plus(minus(times(A,C)),minus(times(A,minus(B))))) = times(A,B),
inference(paramod,[status(thm)],[c_1,c_188]) ).
cnf(c_95,plain,
minus(times(A,minus(B))) = times(A,B),
inference(paramod,[status(thm)],[c_18,c_189]) ).
cnf(c_190,plain,
minus(times(A,B)) = times(A,minus(B)),
inference(paramod,[status(thm)],[c_95,c_31]) ).
cnf(c_101,plain,
times(A,minus(B)) = minus(times(A,B)),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_191,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(times(a,times(c,minus(times(d,b)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_101,c_22]) ).
cnf(c_192,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(times(a,times(c,minus(times(b,d)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_8,c_191]) ).
cnf(c_193,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(times(a,minus(times(c,times(b,d)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_101,c_192]) ).
cnf(c_194,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(times(a,minus(times(b,times(c,d)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_193]) ).
cnf(c_195,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(times(a,times(c,times(d,minus(b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_101,c_194]) ).
cnf(c_196,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(times(a,times(c,minus(times(d,b)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_101,c_195]) ).
cnf(c_197,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(times(a,times(c,minus(times(b,d)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_8,c_196]) ).
cnf(c_198,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(times(a,minus(times(c,times(b,d)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_101,c_197]) ).
cnf(c_199,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(times(a,minus(times(b,times(c,d)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_198]) ).
cnf(c_200,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(d,times(d,times(minus(b),minus(b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_101,c_199]) ).
cnf(c_201,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(d,times(d,minus(times(minus(b),b))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_101,c_200]) ).
cnf(c_202,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(d,times(d,minus(times(b,minus(b)))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_8,c_201]) ).
cnf(c_203,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(d,times(d,minus(minus(times(b,b)))))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_101,c_202]) ).
cnf(c_204,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(d,times(d,times(b,b)))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_31,c_203]) ).
cnf(c_205,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(d,times(b,times(d,b)))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_204]) ).
cnf(c_206,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(d,times(b,times(b,d)))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_8,c_205]) ).
cnf(c_207,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(b,times(d,times(b,d)))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_206]) ).
cnf(c_208,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),times(b,times(b,times(d,d)))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_21,c_207]) ).
cnf(c_209,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(minus(times(a,times(b,times(c,d)))),plus(times(a,times(a,times(d,d))),plus(minus(times(a,times(b,times(c,d)))),times(b,times(b,times(d,d)))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_208]) ).
cnf(c_210,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(times(a,times(b,times(c,d))),plus(minus(times(a,times(b,times(c,d)))),plus(minus(times(a,times(b,times(c,d)))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_15,c_209]) ).
cnf(c_211,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(b,times(c,d))),plus(minus(times(a,times(b,times(c,d)))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_34,c_210]) ).
cnf(c_212,plain,
plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))) != plus(times(a,times(a,times(c,c))),plus(times(b,times(b,times(c,c))),plus(times(a,times(a,times(d,d))),times(b,times(b,times(d,d)))))),
inference(paramod,[status(thm)],[c_18,c_211]) ).
cnf(c_104,plain,
$false,
inference(copy,[status(thm)],[c_212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG131-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:10:38 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 2968163 was started by sandbox2 on n007,
% 0.09/0.38 % Sat Sep 26 06:10:38 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.09/0.43 % Length of proof is 29.
% 0.09/0.43 % Level of proof is 9.
% 0.09/0.43 % Maximum clause weight is 99.000.
% 0.09/0.43 % Given clauses 27.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
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