%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:26:17 AM UTC 2026
% Result : Unsatisfiable 11.79s 3.35s
% Output : CNFRefutation 11.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 81 ( 41 unt; 0 def)
% Number of atoms : 165 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 176 ( 92 ~; 84 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 226 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_1,plain,
sum(additive_identity,A,A),
inference(clausify,[status(thm)],[additive_identity1]) ).
fof(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_2,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
fof(closure_of_multiplication,axiom,
! [VAR_0,VAR_1] : product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_multiplication) ).
cnf(c_3,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_multiplication]) ).
fof(closure_of_addition,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,VAR_1,add(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_addition) ).
cnf(c_4,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
fof(right_inverse,axiom,
! [VAR_0] : sum(VAR_0,additive_inverse(VAR_0),additive_identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_6,plain,
sum(A,additive_inverse(A),additive_identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(associativity_of_addition1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition1) ).
cnf(c_7,plain,
( sum(A,E,F)
| ~ sum(C,D,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition1]) ).
fof(associativity_of_addition2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition2) ).
cnf(c_8,plain,
( sum(C,D,F)
| ~ sum(A,E,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition2]) ).
fof(commutativity_of_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( sum(VAR_1,VAR_0,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_of_addition) ).
cnf(c_9,plain,
( sum(B,A,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity1) ).
cnf(c_12,plain,
( sum(C,E,V6)
| ~ product(A,F,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity1]) ).
fof(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_2,VAR_4,VAR_6)
| ~ sum(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity2) ).
cnf(c_13,plain,
( product(A,F,V6)
| ~ sum(C,E,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity2]) ).
fof(distributivity3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_0,VAR_3,VAR_5)
| ~ product(VAR_3,VAR_1,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity3) ).
cnf(c_14,plain,
( sum(C,E,V6)
| ~ product(F,B,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity3]) ).
fof(addition_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ sum(VAR_0,VAR_1,VAR_3)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',addition_is_well_defined) ).
cnf(c_16,plain,
( C = D
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(a_times_b,axiom,
product(a,b,c),
file('theBenchmark.p',a_times_b) ).
cnf(c_18,plain,
product(a,b,c),
inference(clausify,[status(thm)],[a_times_b]) ).
fof(a_inverse_times_b_inverse,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('theBenchmark.p',a_inverse_times_b_inverse) ).
cnf(c_19,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(clausify,[status(thm)],[a_inverse_times_b_inverse]) ).
fof(prove_c_equals_d,axiom,
c != d,
file('theBenchmark.p',prove_c_equals_d) ).
cnf(c_20,plain,
c != d,
inference(clausify,[status(thm)],[prove_c_equals_d]) ).
cnf(c_21,plain,
d != c,
inference(copy,[status(thm)],[c_20]) ).
cnf(c_3931,plain,
( sum(A,C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_3932,plain,
( sum(A,additive_identity,B)
| ~ sum(additive_identity,additive_inverse(additive_inverse(A)),B) ),
inference(resolve,[status(thm)],[c_3931,c_6]) ).
cnf(c_23,plain,
sum(A,additive_identity,additive_inverse(additive_inverse(A))),
inference(resolve,[status(thm)],[c_3932,c_1]) ).
cnf(c_3933,plain,
( sum(A,C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_3934,plain,
( sum(C,add(additive_inverse(C),A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_3933,c_4]) ).
cnf(c_28,plain,
sum(A,add(additive_inverse(A),B),B),
inference(resolve,[status(thm)],[c_3934,c_1]) ).
cnf(c_3935,plain,
( sum(add(D,A),B,E)
| ~ sum(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_3936,plain,
( sum(add(A,C),additive_inverse(C),B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_3935,c_6]) ).
cnf(c_73,plain,
sum(add(A,B),additive_inverse(B),A),
inference(resolve,[status(thm)],[c_3936,c_2]) ).
cnf(c_93,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_3937,plain,
( sum(multiply(A,D),C,F)
| ~ product(A,E,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_3]) ).
cnf(c_3938,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_3937,c_3]) ).
cnf(c_3939,plain,
( sum(multiply(A,B),multiply(A,C),D)
| ~ product(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_3938,c_4]) ).
cnf(c_98,plain,
sum(multiply(A,B),multiply(A,C),multiply(A,add(B,C))),
inference(resolve,[status(thm)],[c_3939,c_3]) ).
cnf(c_3940,plain,
( sum(multiply(D,B),C,F)
| ~ product(E,B,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_3941,plain,
( sum(multiply(A,D),multiply(B,D),E)
| ~ product(C,D,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_3940,c_3]) ).
cnf(c_3942,plain,
( sum(multiply(A,C),multiply(B,C),D)
| ~ product(add(A,B),C,D) ),
inference(resolve,[status(thm)],[c_3941,c_4]) ).
cnf(c_108,plain,
sum(multiply(A,B),multiply(C,B),multiply(add(A,C),B)),
inference(resolve,[status(thm)],[c_3942,c_3]) ).
cnf(c_3943,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_119,plain,
add(A,additive_identity) = A,
inference(resolve,[status(thm)],[c_3943,c_2]) ).
cnf(c_3944,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_120,plain,
add(additive_identity,A) = A,
inference(resolve,[status(thm)],[c_3944,c_1]) ).
cnf(c_3945,plain,
( B = A
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_16,c_2]) ).
cnf(c_197,plain,
~ sum(c,additive_identity,d),
inference(resolve,[status(thm)],[c_3945,c_21]) ).
cnf(c_3946,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_3947,plain,
add(A,additive_identity) = additive_inverse(additive_inverse(A)),
inference(resolve,[status(thm)],[c_3946,c_23]) ).
cnf(c_3948,plain,
A = additive_inverse(additive_inverse(A)),
inference(paramod,[status(thm)],[c_119,c_3947]) ).
cnf(c_201,plain,
additive_inverse(additive_inverse(A)) = A,
inference(copy,[status(thm)],[c_3948]) ).
cnf(c_3949,plain,
( product(additive_inverse(a),C,D)
| ~ sum(d,B,D)
| ~ sum(additive_inverse(b),A,C)
| ~ product(additive_inverse(a),A,B) ),
inference(resolve,[status(thm)],[c_13,c_19]) ).
cnf(c_3950,plain,
( product(additive_inverse(a),B,C)
| ~ sum(d,multiply(additive_inverse(a),A),C)
| ~ sum(additive_inverse(b),A,B) ),
inference(resolve,[status(thm)],[c_3949,c_3]) ).
cnf(c_3951,plain,
( product(additive_inverse(a),A,B)
| ~ sum(d,multiply(additive_inverse(a),add(additive_inverse(additive_inverse(b)),A)),B) ),
inference(resolve,[status(thm)],[c_3950,c_28]) ).
cnf(c_3952,plain,
product(additive_inverse(a),A,add(d,multiply(additive_inverse(a),add(additive_inverse(additive_inverse(b)),A)))),
inference(resolve,[status(thm)],[c_3951,c_4]) ).
cnf(c_211,plain,
product(additive_inverse(a),A,add(d,multiply(additive_inverse(a),add(b,A)))),
inference(paramod,[status(thm)],[c_201,c_3952]) ).
cnf(c_3953,plain,
( sum(A,B,E)
| ~ sum(D,additive_inverse(C),E)
| ~ sum(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_7,c_73]) ).
cnf(c_3954,plain,
( sum(A,B,D)
| ~ sum(A,add(B,C),add(D,C)) ),
inference(resolve,[status(thm)],[c_3953,c_73]) ).
cnf(c_3955,plain,
~ sum(c,add(additive_identity,A),add(d,A)),
inference(resolve,[status(thm)],[c_3954,c_197]) ).
cnf(c_1110,plain,
~ sum(c,A,add(d,A)),
inference(paramod,[status(thm)],[c_120,c_3955]) ).
cnf(c_3956,plain,
( sum(c,B,D)
| ~ product(C,b,D)
| ~ sum(a,A,C)
| ~ product(A,b,B) ),
inference(resolve,[status(thm)],[c_14,c_18]) ).
cnf(c_3957,plain,
( sum(c,multiply(A,b),C)
| ~ product(B,b,C)
| ~ sum(a,A,B) ),
inference(resolve,[status(thm)],[c_3956,c_3]) ).
cnf(c_3958,plain,
( sum(c,multiply(add(additive_inverse(a),A),b),B)
| ~ product(A,b,B) ),
inference(resolve,[status(thm)],[c_3957,c_28]) ).
cnf(c_2011,plain,
~ product(A,b,add(d,multiply(add(additive_inverse(a),A),b))),
inference(resolve,[status(thm)],[c_3958,c_1110]) ).
cnf(c_3959,plain,
( add(B,A) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_93]) ).
cnf(c_3960,plain,
add(multiply(A,B),multiply(A,C)) = multiply(A,add(C,B)),
inference(resolve,[status(thm)],[c_3959,c_98]) ).
cnf(c_2607,plain,
multiply(A,add(B,C)) = add(multiply(A,C),multiply(A,B)),
inference(copy,[status(thm)],[c_3960]) ).
cnf(c_2685,plain,
product(additive_inverse(a),A,add(d,add(multiply(additive_inverse(a),A),multiply(additive_inverse(a),b)))),
inference(paramod,[status(thm)],[c_2607,c_211]) ).
cnf(c_3961,plain,
( add(B,A) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_93]) ).
cnf(c_3962,plain,
add(multiply(A,B),multiply(C,B)) = multiply(add(C,A),B),
inference(resolve,[status(thm)],[c_3961,c_108]) ).
cnf(c_3861,plain,
multiply(add(A,B),C) = add(multiply(B,C),multiply(A,C)),
inference(copy,[status(thm)],[c_3962]) ).
cnf(c_3929,plain,
~ product(A,b,add(d,add(multiply(A,b),multiply(additive_inverse(a),b)))),
inference(paramod,[status(thm)],[c_3861,c_2011]) ).
cnf(c_3930,plain,
$false,
inference(resolve,[status(thm)],[c_3929,c_2685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.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 : Sat Sep 26 05:44:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 771851 was started by sandbox on n020,
% 0.08/0.36 % Sat Sep 26 05:44:18 2026
% 0.08/0.36 % 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).
% 11.79/3.35
% 11.79/3.35 % SZS status Unsatisfiable for theBenchmark
% 11.79/3.35
% 11.79/3.35 % Proof 1 at 1.13 (+ 0.38) seconds.
% 11.79/3.35 % Length of proof is 34.
% 11.79/3.35 % Level of proof is 6.
% 11.79/3.35 % Maximum clause weight is 27.000.
% 11.79/3.35 % Given clauses 109.
% 11.79/3.35
% 11.79/3.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------