%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 08:26:16 AM UTC 2026
% Result : Unsatisfiable 2.45s 0.88s
% Output : CNFRefutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 21 unt; 0 def)
% Number of atoms : 98 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 59 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn 37 !; 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(left_inverse,axiom,
! [VAR_0] : sum(additive_inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_5,plain,
sum(additive_inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[left_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(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(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(prove_a_times_0_is_0,axiom,
~ product(a,additive_identity,additive_identity),
file('theBenchmark.p',prove_a_times_0_is_0) ).
cnf(c_18,plain,
~ product(a,additive_identity,additive_identity),
inference(clausify,[status(thm)],[prove_a_times_0_is_0]) ).
cnf(c_1105,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_1106,plain,
( sum(add(A,additive_inverse(C)),C,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_1105,c_5]) ).
cnf(c_73,plain,
sum(add(A,additive_inverse(B)),B,A),
inference(resolve,[status(thm)],[c_1106,c_2]) ).
cnf(c_1107,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_1108,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_1107,c_3]) ).
cnf(c_1109,plain,
( sum(multiply(A,B),multiply(A,additive_identity),C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_1108,c_2]) ).
cnf(c_96,plain,
sum(multiply(A,B),multiply(A,additive_identity),multiply(A,B)),
inference(resolve,[status(thm)],[c_1109,c_3]) ).
cnf(c_1110,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_117,plain,
add(additive_identity,A) = A,
inference(resolve,[status(thm)],[c_1110,c_1]) ).
cnf(c_1111,plain,
( product(A,E,F)
| ~ sum(multiply(A,D),C,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_1112,plain,
( product(D,C,E)
| ~ sum(multiply(D,A),multiply(D,B),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_1111,c_3]) ).
cnf(c_1113,plain,
( product(A,B,C)
| ~ sum(multiply(A,B),multiply(A,additive_identity),C) ),
inference(resolve,[status(thm)],[c_1112,c_2]) ).
cnf(c_127,plain,
~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
inference(resolve,[status(thm)],[c_1113,c_18]) ).
cnf(c_1114,plain,
( sum(add(D,additive_inverse(A)),C,E)
| ~ sum(D,B,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_73]) ).
cnf(c_1115,plain,
( sum(add(A,additive_inverse(multiply(B,D))),multiply(B,D),C)
| ~ sum(A,multiply(B,additive_identity),C) ),
inference(resolve,[status(thm)],[c_1114,c_96]) ).
cnf(c_1116,plain,
sum(add(additive_identity,additive_inverse(multiply(A,B))),multiply(A,B),multiply(A,additive_identity)),
inference(resolve,[status(thm)],[c_1115,c_1]) ).
cnf(c_1084,plain,
sum(additive_inverse(multiply(A,B)),multiply(A,B),multiply(A,additive_identity)),
inference(paramod,[status(thm)],[c_117,c_1116]) ).
cnf(c_1117,plain,
( sum(D,multiply(B,additive_identity),E)
| ~ sum(A,multiply(B,C),E)
| ~ sum(A,multiply(B,C),D) ),
inference(resolve,[status(thm)],[c_8,c_96]) ).
cnf(c_1118,plain,
( sum(D,multiply(B,additive_identity),A)
| ~ sum(add(A,additive_inverse(multiply(B,C))),multiply(B,C),D) ),
inference(resolve,[status(thm)],[c_1117,c_73]) ).
cnf(c_1119,plain,
~ sum(add(additive_identity,additive_inverse(multiply(a,A))),multiply(a,A),multiply(a,additive_identity)),
inference(resolve,[status(thm)],[c_1118,c_127]) ).
cnf(c_1103,plain,
~ sum(additive_inverse(multiply(a,A)),multiply(a,A),multiply(a,additive_identity)),
inference(paramod,[status(thm)],[c_117,c_1119]) ).
cnf(c_1104,plain,
$false,
inference(resolve,[status(thm)],[c_1103,c_1084]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n018.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 05:45:08 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 3853839 was started by sandbox2 on n018,
% 0.19/0.46 % Sat Sep 26 05:45:08 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 2.45/0.88
% 2.45/0.88 % SZS status Unsatisfiable for theBenchmark
% 2.45/0.88
% 2.45/0.88 % Proof 1 at 0.28 (+ 0.12) seconds.
% 2.45/0.88 % Length of proof is 18.
% 2.45/0.88 % Level of proof is 3.
% 2.45/0.88 % Maximum clause weight is 26.000.
% 2.45/0.88 % Given clauses 43.
% 2.45/0.88
% 2.45/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------