%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD052-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 07:11:37 AM UTC 2026
% Result : Unsatisfiable 82.39s 23.10s
% Output : CNFRefutation 82.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 27
% Syntax : Number of formulae : 116 ( 68 unt; 0 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 202 ( 111 ~; 91 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-1 aty)
% Number of variables : 139 ( 7 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_3,VAR_5,VAR_2)
| ~ sum(VAR_4,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_2) ).
cnf(c_2,plain,
( ~ sum(D,F,C)
| ~ sum(E,B,F)
| ~ sum(D,E,A)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_2]) ).
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(associativity_multiplication_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ product(VAR_4,VAR_5,VAR_2)
| ~ product(VAR_3,VAR_5,VAR_1)
| ~ product(VAR_0,VAR_3,VAR_4)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_multiplication_1) ).
cnf(c_6,plain,
( ~ product(E,F,C)
| ~ product(D,F,B)
| ~ product(A,D,E)
| product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_multiplication_1]) ).
fof(associativity_multiplication_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ product(VAR_3,VAR_5,VAR_2)
| ~ product(VAR_4,VAR_1,VAR_5)
| ~ product(VAR_3,VAR_4,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_multiplication_2) ).
cnf(c_7,plain,
( ~ product(D,F,C)
| ~ product(E,B,F)
| ~ product(D,E,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_multiplication_2]) ).
fof(existence_of_identity_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| product(multiplicative_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_multiplication) ).
cnf(c_8,plain,
( ~ defined(A)
| product(multiplicative_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_multiplication]) ).
fof(existence_of_inverse_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,additive_identity)
| product(multiplicative_inverse(VAR_0),VAR_0,multiplicative_identity) ),
file('theBenchmark.p',existence_of_inverse_multiplication) ).
cnf(c_9,plain,
( ~ defined(A)
| sum(additive_identity,A,additive_identity)
| product(multiplicative_inverse(A),A,multiplicative_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_multiplication]) ).
fof(commutativity_multiplication,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ product(VAR_1,VAR_0,VAR_2)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_multiplication) ).
cnf(c_10,plain,
( ~ product(B,A,C)
| product(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_multiplication]) ).
fof(distributivity_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ product(VAR_4,VAR_6,VAR_1)
| ~ product(VAR_3,VAR_6,VAR_0)
| ~ product(VAR_5,VAR_6,VAR_2)
| ~ sum(VAR_3,VAR_4,VAR_5)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity_1) ).
cnf(c_11,plain,
( ~ product(E,V6,B)
| ~ product(D,V6,A)
| ~ product(F,V6,C)
| ~ sum(D,E,F)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[distributivity_1]) ).
fof(distributivity_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ sum(VAR_5,VAR_6,VAR_2)
| ~ product(VAR_4,VAR_1,VAR_6)
| ~ product(VAR_3,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity_2) ).
cnf(c_12,plain,
( ~ sum(F,V6,C)
| ~ product(E,B,V6)
| ~ product(D,B,F)
| ~ sum(D,E,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity_2]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_14,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_identity]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_28,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(c_is_defined,axiom,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(c_29,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(d_is_defined,axiom,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(c_30,plain,
defined(d),
inference(clausify,[status(thm)],[d_is_defined]) ).
fof(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_31,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(l_is_defined,axiom,
defined(l),
file('theBenchmark.p',l_is_defined) ).
cnf(c_34,plain,
defined(l),
inference(clausify,[status(thm)],[l_is_defined]) ).
fof(not_sum_13,axiom,
~ sum(additive_identity,b,additive_identity),
file('theBenchmark.p',not_sum_13) ).
cnf(c_39,plain,
~ sum(additive_identity,b,additive_identity),
inference(clausify,[status(thm)],[not_sum_13]) ).
fof(not_sum_14,axiom,
~ sum(additive_identity,d,additive_identity),
file('theBenchmark.p',not_sum_14) ).
cnf(c_40,plain,
~ sum(additive_identity,d,additive_identity),
inference(clausify,[status(thm)],[not_sum_14]) ).
fof(product_15,axiom,
product(a,multiplicative_inverse(b),s),
file('theBenchmark.p',product_15) ).
cnf(c_41,plain,
product(a,multiplicative_inverse(b),s),
inference(clausify,[status(thm)],[product_15]) ).
fof(product_16,axiom,
product(c,multiplicative_inverse(d),t),
file('theBenchmark.p',product_16) ).
cnf(c_42,plain,
product(c,multiplicative_inverse(d),t),
inference(clausify,[status(thm)],[product_16]) ).
fof(sum_17,axiom,
sum(s,t,u),
file('theBenchmark.p',sum_17) ).
cnf(c_43,plain,
sum(s,t,u),
inference(clausify,[status(thm)],[sum_17]) ).
fof(product_18,axiom,
product(a,d,p),
file('theBenchmark.p',product_18) ).
cnf(c_44,plain,
product(a,d,p),
inference(clausify,[status(thm)],[product_18]) ).
fof(product_19,axiom,
product(b,c,q),
file('theBenchmark.p',product_19) ).
cnf(c_45,plain,
product(b,c,q),
inference(clausify,[status(thm)],[product_19]) ).
fof(sum_20,axiom,
sum(p,q,k),
file('theBenchmark.p',sum_20) ).
cnf(c_46,plain,
sum(p,q,k),
inference(clausify,[status(thm)],[sum_20]) ).
fof(product_21,axiom,
product(b,d,l),
file('theBenchmark.p',product_21) ).
cnf(c_47,plain,
product(b,d,l),
inference(clausify,[status(thm)],[product_21]) ).
fof(not_product_22,axiom,
~ product(k,multiplicative_inverse(l),u),
file('theBenchmark.p',not_product_22) ).
cnf(c_48,plain,
~ product(k,multiplicative_inverse(l),u),
inference(clausify,[status(thm)],[not_product_22]) ).
cnf(c_51,plain,
( ~ sum(D,B,D)
| ~ sum(C,D,A)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_57,plain,
( ~ product(D,E,B)
| ~ product(C,E,A)
| ~ sum(C,D,C)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_70,plain,
( ~ product(B,C,A)
| ~ sum(B,B,B)
| sum(A,A,A) ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_75,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_77,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_132,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_15397,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_169,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_39,c_15397]) ).
cnf(c_170,plain,
product(multiplicative_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_171,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_217,plain,
product(multiplicative_identity,c,c),
inference(resolve,[status(thm)],[c_29,c_8]) ).
cnf(c_15398,plain,
( sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_30,c_9]) ).
cnf(c_272,plain,
product(multiplicative_inverse(d),d,multiplicative_identity),
inference(resolve,[status(thm)],[c_40,c_15398]) ).
cnf(c_338,plain,
product(multiplicative_identity,u,u),
inference(resolve,[status(thm)],[c_31,c_8]) ).
cnf(c_586,plain,
( sum(additive_identity,l,additive_identity)
| product(multiplicative_inverse(l),l,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_34,c_9]) ).
cnf(c_587,plain,
product(multiplicative_identity,l,l),
inference(resolve,[status(thm)],[c_34,c_8]) ).
cnf(c_589,plain,
sum(additive_identity,l,l),
inference(resolve,[status(thm)],[c_34,c_3]) ).
cnf(c_1238,plain,
product(c,b,q),
inference(resolve,[status(thm)],[c_45,c_10]) ).
cnf(c_1266,plain,
product(d,b,l),
inference(resolve,[status(thm)],[c_47,c_10]) ).
cnf(c_1276,plain,
~ product(multiplicative_inverse(l),k,u),
inference(resolve,[status(thm)],[c_10,c_48]) ).
cnf(c_1346,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_75,c_10]) ).
cnf(c_1789,plain,
product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_132,c_10]) ).
cnf(c_1829,plain,
product(b,multiplicative_identity,b),
inference(resolve,[status(thm)],[c_170,c_10]) ).
cnf(c_2042,plain,
product(c,multiplicative_identity,c),
inference(resolve,[status(thm)],[c_217,c_10]) ).
cnf(c_2417,plain,
product(l,multiplicative_identity,l),
inference(resolve,[status(thm)],[c_587,c_10]) ).
cnf(c_15399,plain,
( ~ product(a,C,B)
| ~ product(multiplicative_inverse(b),A,C)
| product(s,A,B) ),
inference(resolve,[status(thm)],[c_7,c_41]) ).
cnf(c_15400,plain,
( ~ product(a,multiplicative_identity,A)
| product(s,b,A) ),
inference(resolve,[status(thm)],[c_15399,c_169]) ).
cnf(c_12294,plain,
product(s,b,a),
inference(resolve,[status(thm)],[c_15400,c_1789]) ).
cnf(c_15401,plain,
( ~ sum(B,b,B)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_51,c_39]) ).
cnf(c_12333,plain,
~ sum(b,b,b),
inference(resolve,[status(thm)],[c_15401,c_171]) ).
cnf(c_15402,plain,
( ~ product(A,B,b)
| ~ sum(A,A,A) ),
inference(resolve,[status(thm)],[c_70,c_12333]) ).
cnf(c_12377,plain,
~ product(additive_identity,A,b),
inference(resolve,[status(thm)],[c_15402,c_77]) ).
cnf(c_15403,plain,
( ~ product(a,C,B)
| ~ product(b,C,A)
| product(s,A,B) ),
inference(resolve,[status(thm)],[c_6,c_12294]) ).
cnf(c_15404,plain,
( ~ product(a,d,A)
| product(s,l,A) ),
inference(resolve,[status(thm)],[c_15403,c_47]) ).
cnf(c_12404,plain,
product(s,l,p),
inference(resolve,[status(thm)],[c_15404,c_44]) ).
cnf(c_12511,plain,
~ product(A,additive_identity,b),
inference(resolve,[status(thm)],[c_10,c_12377]) ).
cnf(c_15405,plain,
( ~ product(c,C,B)
| ~ product(multiplicative_inverse(d),A,C)
| product(t,A,B) ),
inference(resolve,[status(thm)],[c_7,c_42]) ).
cnf(c_15406,plain,
( ~ product(c,multiplicative_identity,A)
| product(t,d,A) ),
inference(resolve,[status(thm)],[c_15405,c_272]) ).
cnf(c_15119,plain,
product(t,d,c),
inference(resolve,[status(thm)],[c_15406,c_2042]) ).
cnf(c_15407,plain,
( ~ product(C,D,b)
| ~ product(B,D,additive_identity)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_12511]) ).
cnf(c_15408,plain,
( ~ product(multiplicative_identity,A,b)
| ~ product(d,A,additive_identity) ),
inference(resolve,[status(thm)],[c_15407,c_272]) ).
cnf(c_15167,plain,
~ product(d,b,additive_identity),
inference(resolve,[status(thm)],[c_15408,c_170]) ).
cnf(c_15409,plain,
( ~ product(B,C,additive_identity)
| ~ product(A,C,b)
| ~ product(d,A,B) ),
inference(resolve,[status(thm)],[c_6,c_15167]) ).
cnf(c_15410,plain,
( ~ product(l,A,additive_identity)
| ~ product(b,A,b) ),
inference(resolve,[status(thm)],[c_15409,c_1266]) ).
cnf(c_15175,plain,
~ product(l,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_15410,c_1829]) ).
cnf(c_15411,plain,
( ~ product(c,C,B)
| ~ product(d,C,A)
| product(t,A,B) ),
inference(resolve,[status(thm)],[c_6,c_15119]) ).
cnf(c_15412,plain,
( ~ product(c,b,A)
| product(t,l,A) ),
inference(resolve,[status(thm)],[c_15411,c_1266]) ).
cnf(c_15199,plain,
product(t,l,q),
inference(resolve,[status(thm)],[c_15412,c_1238]) ).
cnf(c_15413,plain,
( ~ sum(C,D,B)
| ~ product(t,A,D)
| ~ product(s,A,C)
| product(u,A,B) ),
inference(resolve,[status(thm)],[c_12,c_43]) ).
cnf(c_15414,plain,
( ~ sum(p,B,A)
| ~ product(t,l,B)
| product(u,l,A) ),
inference(resolve,[status(thm)],[c_15413,c_12404]) ).
cnf(c_15415,plain,
( ~ sum(p,q,A)
| product(u,l,A) ),
inference(resolve,[status(thm)],[c_15414,c_15199]) ).
cnf(c_15252,plain,
product(u,l,k),
inference(resolve,[status(thm)],[c_15415,c_46]) ).
cnf(c_15416,plain,
( ~ sum(C,D,additive_identity)
| ~ product(B,multiplicative_identity,D)
| ~ product(A,multiplicative_identity,C)
| ~ sum(A,B,l) ),
inference(resolve,[status(thm)],[c_12,c_15175]) ).
cnf(c_15417,plain,
( ~ sum(A,B,additive_identity)
| ~ product(l,multiplicative_identity,B)
| ~ product(additive_identity,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_15416,c_589]) ).
cnf(c_15418,plain,
( ~ sum(additive_identity,A,additive_identity)
| ~ product(l,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_15417,c_1346]) ).
cnf(c_15349,plain,
~ sum(additive_identity,l,additive_identity),
inference(resolve,[status(thm)],[c_15418,c_2417]) ).
cnf(c_15353,plain,
product(multiplicative_inverse(l),l,multiplicative_identity),
inference(resolve,[status(thm)],[c_15349,c_586]) ).
cnf(c_15372,plain,
product(l,u,k),
inference(resolve,[status(thm)],[c_15252,c_10]) ).
cnf(c_15419,plain,
( ~ product(B,C,u)
| ~ product(A,C,k)
| ~ product(multiplicative_inverse(l),A,B) ),
inference(resolve,[status(thm)],[c_6,c_1276]) ).
cnf(c_15420,plain,
( ~ product(A,u,u)
| ~ product(multiplicative_inverse(l),l,A) ),
inference(resolve,[status(thm)],[c_15419,c_15372]) ).
cnf(c_15421,plain,
~ product(multiplicative_inverse(l),l,multiplicative_identity),
inference(resolve,[status(thm)],[c_15420,c_338]) ).
cnf(c_15396,plain,
$false,
inference(resolve,[status(thm)],[c_15353,c_15421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD052-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 02:32:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 88843 was started by sandbox on n003,
% 0.10/0.37 % Sun Sep 27 02:32:25 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 82.39/23.10
% 82.39/23.10 % given #500 (A,wt=16): 164 defined(multiply(A,b)) | -defined(A). [resolve(28,a,16,c)].
% 82.39/23.10
% 82.39/23.10 % given #1000 (F,wt=9): 15234 -product(additive_identity,t,d). [ur(58,a,14263,a,b,275,a,c,15191,a)].
% 82.39/23.10
% 82.39/23.10 % SZS status Unsatisfiable for theBenchmark
% 82.39/23.10
% 82.39/23.10 % Proof 1 at 2.32 (+ 0.80) seconds.
% 82.39/23.10 % Length of proof is 64.
% 82.39/23.10 % Level of proof is 9.
% 82.39/23.10 % Maximum clause weight is 25.000.
% 82.39/23.10 % Given clauses 1002.
% 82.39/23.10
% 82.39/23.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------