%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG004-2 : 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 : 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 08:26:17 AM UTC 2026
% Result : Unsatisfiable 5.23s 6.15s
% Output : CNFRefutation 5.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 86 ( 49 unt; 0 def)
% Number of atoms : 159 ( 44 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 149 ( 76 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 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 : 210 ( 6 sgn 53 !; 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(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(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(multiplication_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',multiplication_is_well_defined) ).
cnf(c_17,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[multiplication_is_well_defined]) ).
fof(cancellation1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_3
| ~ sum(VAR_0,VAR_3,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cancellation1) ).
cnf(c_18,plain,
( B = D
| ~ sum(A,D,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[cancellation1]) ).
fof(cancellation2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_3
| ~ sum(VAR_3,VAR_1,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cancellation2) ).
cnf(c_19,plain,
( A = D
| ~ sum(D,B,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[cancellation2]) ).
fof(a_times_b,axiom,
product(a,b,c),
file('theBenchmark.p',a_times_b) ).
cnf(c_20,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_21,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_22,plain,
c != d,
inference(clausify,[status(thm)],[prove_c_equals_d]) ).
cnf(c_23,plain,
d != c,
inference(copy,[status(thm)],[c_22]) ).
cnf(c_2360,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_2361,plain,
( sum(C,add(additive_inverse(C),A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_2360,c_4]) ).
cnf(c_30,plain,
sum(A,add(additive_inverse(A),B),B),
inference(resolve,[status(thm)],[c_2361,c_1]) ).
cnf(c_2362,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_2363,plain,
( sum(add(A,additive_inverse(C)),C,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_2362,c_5]) ).
cnf(c_78,plain,
sum(add(A,additive_inverse(B)),B,A),
inference(resolve,[status(thm)],[c_2363,c_2]) ).
cnf(c_95,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_2364,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_2365,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_2364,c_3]) ).
cnf(c_2366,plain,
( sum(multiply(A,C),multiply(A,additive_inverse(C)),B)
| ~ product(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_2365,c_6]) ).
cnf(c_98,plain,
sum(multiply(A,B),multiply(A,additive_inverse(B)),multiply(A,additive_identity)),
inference(resolve,[status(thm)],[c_2366,c_3]) ).
cnf(c_2367,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_2368,plain,
( sum(multiply(A,D),multiply(B,D),E)
| ~ product(C,D,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_2367,c_3]) ).
cnf(c_2369,plain,
( sum(multiply(C,A),multiply(additive_inverse(C),A),B)
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_2368,c_6]) ).
cnf(c_108,plain,
sum(multiply(A,B),multiply(additive_inverse(A),B),multiply(additive_identity,B)),
inference(resolve,[status(thm)],[c_2369,c_3]) ).
cnf(c_2370,plain,
( additive_identity = B
| ~ sum(A,additive_inverse(A),B) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_2371,plain,
additive_identity = additive_inverse(additive_identity),
inference(resolve,[status(thm)],[c_2370,c_1]) ).
cnf(c_119,plain,
additive_inverse(additive_identity) = additive_identity,
inference(copy,[status(thm)],[c_2371]) ).
cnf(c_2372,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_122,plain,
add(additive_identity,A) = A,
inference(resolve,[status(thm)],[c_2372,c_1]) ).
cnf(c_2373,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_124,plain,
multiply(a,b) = c,
inference(resolve,[status(thm)],[c_2373,c_20]) ).
cnf(c_2374,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_157,plain,
multiply(additive_inverse(a),additive_inverse(b)) = d,
inference(resolve,[status(thm)],[c_2374,c_21]) ).
cnf(c_2375,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_420,plain,
add(A,B) = add(B,A),
inference(resolve,[status(thm)],[c_2375,c_95]) ).
cnf(c_2376,plain,
( additive_identity = B
| ~ sum(A,B,A) ),
inference(resolve,[status(thm)],[c_18,c_2]) ).
cnf(c_2377,plain,
additive_identity = multiply(A,additive_inverse(additive_identity)),
inference(resolve,[status(thm)],[c_2376,c_98]) ).
cnf(c_2378,plain,
additive_identity = multiply(A,additive_identity),
inference(paramod,[status(thm)],[c_119,c_2377]) ).
cnf(c_1388,plain,
multiply(A,additive_identity) = additive_identity,
inference(copy,[status(thm)],[c_2378]) ).
cnf(c_2379,plain,
( multiply(A,additive_inverse(B)) = C
| ~ sum(multiply(A,B),C,multiply(A,additive_identity)) ),
inference(resolve,[status(thm)],[c_18,c_98]) ).
cnf(c_2380,plain,
multiply(A,additive_inverse(B)) = add(additive_inverse(multiply(A,B)),multiply(A,additive_identity)),
inference(resolve,[status(thm)],[c_2379,c_30]) ).
cnf(c_2381,plain,
multiply(A,additive_inverse(B)) = add(additive_inverse(multiply(A,B)),additive_identity),
inference(paramod,[status(thm)],[c_1388,c_2380]) ).
cnf(c_2382,plain,
multiply(A,additive_inverse(B)) = add(additive_identity,additive_inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_420,c_2381]) ).
cnf(c_2383,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(paramod,[status(thm)],[c_122,c_2382]) ).
cnf(c_1389,plain,
additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
inference(copy,[status(thm)],[c_2383]) ).
cnf(c_2384,plain,
( add(C,additive_inverse(B)) = A
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_19,c_78]) ).
cnf(c_2385,plain,
add(multiply(additive_identity,A),additive_inverse(multiply(additive_inverse(B),A))) = multiply(B,A),
inference(resolve,[status(thm)],[c_2384,c_108]) ).
cnf(c_2229,plain,
add(multiply(additive_identity,A),multiply(additive_inverse(B),additive_inverse(A))) = multiply(B,A),
inference(paramod,[status(thm)],[c_1389,c_2385]) ).
cnf(c_2386,plain,
( additive_identity = B
| ~ sum(A,B,A) ),
inference(resolve,[status(thm)],[c_18,c_2]) ).
cnf(c_2387,plain,
additive_identity = multiply(additive_inverse(additive_identity),A),
inference(resolve,[status(thm)],[c_2386,c_108]) ).
cnf(c_2388,plain,
additive_identity = multiply(additive_identity,A),
inference(paramod,[status(thm)],[c_119,c_2387]) ).
cnf(c_2231,plain,
multiply(additive_identity,A) = additive_identity,
inference(copy,[status(thm)],[c_2388]) ).
cnf(c_2389,plain,
add(additive_identity,multiply(additive_inverse(B),additive_inverse(A))) = multiply(B,A),
inference(paramod,[status(thm)],[c_2231,c_2229]) ).
cnf(c_2305,plain,
multiply(additive_inverse(A),additive_inverse(B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_122,c_2389]) ).
cnf(c_2390,plain,
multiply(a,b) = d,
inference(paramod,[status(thm)],[c_2305,c_157]) ).
cnf(c_2391,plain,
c = d,
inference(paramod,[status(thm)],[c_124,c_2390]) ).
cnf(c_2358,plain,
d = c,
inference(copy,[status(thm)],[c_2391]) ).
cnf(c_2359,plain,
$false,
inference(resolve,[status(thm)],[c_2358,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.46 % Computer : n018.cluster.edu
% 0.17/5.46 % Model : x86_64 x86_64
% 0.17/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.46 % Memory : 8046.5625MB
% 0.17/5.46 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Sat Sep 26 05:45:57 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.46 % Process 3855455 was started by sandbox on n018,
% 0.17/5.46 % Sat Sep 26 05:45:57 2026
% 0.17/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.47
% 0.17/5.47 % From the command line: assign(max_seconds, 300).
% 5.23/6.15
% 5.23/6.15 % SZS status Unsatisfiable for theBenchmark
% 5.23/6.15
% 5.23/6.15 % Proof 1 at 0.47 (+ 0.19) seconds.
% 5.23/6.15 % Length of proof is 36.
% 5.23/6.15 % Level of proof is 7.
% 5.23/6.15 % Maximum clause weight is 33.000.
% 5.23/6.15 % Given clauses 77.
% 5.23/6.15
% 5.23/6.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------