%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG039-1 : 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 : n009.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 08:26:28 AM UTC 2026
% Result : Unsatisfiable 4.80s 1.11s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 46 unt; 0 def)
% Number of atoms : 129 ( 21 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 123 ( 66 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 155 ( 17 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(distributivity4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_2,VAR_4,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',distributivity4) ).
cnf(c_15,plain,
( product(F,B,V6)
| ~ sum(C,E,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity4]) ).
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(absorbtion1,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,add(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',absorbtion1) ).
cnf(c_18,plain,
sum(A,add(A,B),B),
inference(clausify,[status(thm)],[absorbtion1]) ).
fof(clause32,axiom,
! [VAR_0] : sum(VAR_0,VAR_0,additive_identity),
file('theBenchmark.p',clause32) ).
cnf(c_20,plain,
sum(A,A,additive_identity),
inference(clausify,[status(thm)],[clause32]) ).
fof(clause33,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',clause33) ).
cnf(c_21,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[clause33]) ).
fof(clause35,axiom,
! [VAR_0] : multiply(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',clause35) ).
cnf(c_23,plain,
multiply(A,A) = A,
inference(clausify,[status(thm)],[clause35]) ).
fof(clause36,axiom,
multiply(a,b) = c,
file('theBenchmark.p',clause36) ).
cnf(c_24,plain,
multiply(a,b) = c,
inference(clausify,[status(thm)],[clause36]) ).
cnf(c_25,plain,
c = multiply(a,b),
inference(copy,[status(thm)],[c_24]) ).
fof(clause37,axiom,
multiply(b,a) = d,
file('theBenchmark.p',clause37) ).
cnf(c_26,plain,
multiply(b,a) = d,
inference(clausify,[status(thm)],[clause37]) ).
cnf(c_27,plain,
d = multiply(b,a),
inference(copy,[status(thm)],[c_26]) ).
fof(clause43,axiom,
! [VAR_0,VAR_1] : product(VAR_0,multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_1)),
file('theBenchmark.p',clause43) ).
cnf(c_37,plain,
product(A,multiply(A,B),multiply(A,B)),
inference(clausify,[status(thm)],[clause43]) ).
fof(clause44,axiom,
! [VAR_0,VAR_1] : product(a,multiply(b,VAR_0),multiply(VAR_1,VAR_0)),
file('theBenchmark.p',clause44) ).
cnf(c_38,plain,
product(a,multiply(b,A),multiply(B,A)),
inference(clausify,[status(thm)],[clause44]) ).
fof(clause71,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',clause71) ).
cnf(c_82,plain,
product(A,A,A),
inference(clausify,[status(thm)],[clause71]) ).
fof(prove_c_equals_d,axiom,
c != d,
file('theBenchmark.p',prove_c_equals_d) ).
cnf(c_85,plain,
c != d,
inference(clausify,[status(thm)],[prove_c_equals_d]) ).
cnf(c_2103,plain,
multiply(a,b) != d,
inference(paramod,[status(thm)],[c_25,c_85]) ).
cnf(c_2104,plain,
multiply(a,b) != multiply(b,a),
inference(paramod,[status(thm)],[c_27,c_2103]) ).
cnf(c_86,plain,
multiply(b,a) != multiply(a,b),
inference(copy,[status(thm)],[c_2104]) ).
cnf(c_165,plain,
sum(add(A,B),A,B),
inference(resolve,[status(thm)],[c_9,c_18]) ).
cnf(c_2105,plain,
( sum(B,C,E)
| ~ sum(A,D,E)
| ~ sum(add(A,B),C,D) ),
inference(resolve,[status(thm)],[c_8,c_18]) ).
cnf(c_2106,plain,
( sum(D,add(add(A,D),B),C)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_2105,c_18]) ).
cnf(c_2107,plain,
sum(A,add(add(B,A),additive_identity),B),
inference(resolve,[status(thm)],[c_2106,c_2]) ).
cnf(c_173,plain,
sum(A,add(B,A),B),
inference(paramod,[status(thm)],[c_21,c_2107]) ).
cnf(c_2108,plain,
( product(E,B,F)
| ~ sum(multiply(D,B),C,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_2109,plain,
( product(C,D,E)
| ~ sum(multiply(A,D),multiply(B,D),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_2108,c_3]) ).
cnf(c_2110,plain,
( product(additive_identity,B,C)
| ~ sum(multiply(A,B),multiply(A,B),C) ),
inference(resolve,[status(thm)],[c_2109,c_20]) ).
cnf(c_230,plain,
product(additive_identity,A,additive_identity),
inference(resolve,[status(thm)],[c_2110,c_20]) ).
cnf(c_511,plain,
product(a,b,multiply(A,b)),
inference(paramod,[status(thm)],[c_23,c_38]) ).
cnf(c_2111,plain,
( C = multiply(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_1155,plain,
~ product(a,b,multiply(b,a)),
inference(resolve,[status(thm)],[c_2111,c_86]) ).
cnf(c_2112,plain,
( product(E,B,F)
| ~ sum(multiply(D,B),C,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_2113,plain,
( product(B,b,D)
| ~ sum(multiply(A,b),multiply(C,b),D)
| ~ sum(A,a,B) ),
inference(resolve,[status(thm)],[c_2112,c_511]) ).
cnf(c_2114,plain,
( product(A,b,C)
| ~ sum(multiply(add(a,A),b),multiply(B,b),C) ),
inference(resolve,[status(thm)],[c_2113,c_165]) ).
cnf(c_1939,plain,
product(A,b,additive_identity),
inference(resolve,[status(thm)],[c_2114,c_20]) ).
cnf(c_2115,plain,
( A = B
| ~ product(A,A,B) ),
inference(resolve,[status(thm)],[c_17,c_82]) ).
cnf(c_2116,plain,
b = additive_identity,
inference(resolve,[status(thm)],[c_2115,c_1939]) ).
cnf(c_2026,plain,
additive_identity = b,
inference(copy,[status(thm)],[c_2116]) ).
cnf(c_2117,plain,
( sum(additive_identity,B,E)
| ~ product(additive_identity,D,E)
| ~ sum(C,A,D)
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_12,c_230]) ).
cnf(c_2118,plain,
( sum(additive_identity,additive_identity,C)
| ~ product(additive_identity,B,C)
| ~ sum(A,b,B) ),
inference(resolve,[status(thm)],[c_2117,c_1939]) ).
cnf(c_2119,plain,
( sum(additive_identity,additive_identity,B)
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_2118,c_165]) ).
cnf(c_2120,plain,
sum(additive_identity,additive_identity,multiply(additive_identity,A)),
inference(resolve,[status(thm)],[c_2119,c_37]) ).
cnf(c_2121,plain,
sum(b,additive_identity,multiply(additive_identity,A)),
inference(paramod,[status(thm)],[c_2026,c_2120]) ).
cnf(c_2122,plain,
sum(b,b,multiply(additive_identity,A)),
inference(paramod,[status(thm)],[c_2026,c_2121]) ).
cnf(c_2066,plain,
sum(b,b,multiply(b,A)),
inference(paramod,[status(thm)],[c_2026,c_2122]) ).
cnf(c_2123,plain,
( product(D,b,E)
| ~ sum(additive_identity,B,E)
| ~ sum(C,A,D)
| ~ product(A,b,B) ),
inference(resolve,[status(thm)],[c_15,c_1939]) ).
cnf(c_2124,plain,
( product(C,b,D)
| ~ sum(additive_identity,additive_identity,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_2123,c_1939]) ).
cnf(c_2125,plain,
( product(B,b,A)
| ~ sum(additive_identity,additive_identity,A) ),
inference(resolve,[status(thm)],[c_2124,c_173]) ).
cnf(c_2126,plain,
~ sum(additive_identity,additive_identity,multiply(b,a)),
inference(resolve,[status(thm)],[c_2125,c_1155]) ).
cnf(c_2127,plain,
~ sum(b,additive_identity,multiply(b,a)),
inference(paramod,[status(thm)],[c_2026,c_2126]) ).
cnf(c_2101,plain,
~ sum(b,b,multiply(b,a)),
inference(paramod,[status(thm)],[c_2026,c_2127]) ).
cnf(c_2102,plain,
$false,
inference(resolve,[status(thm)],[c_2101,c_2066]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.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 05:51:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 3503874 was started by sandbox2 on n009,
% 0.09/0.38 % Sat Sep 26 05:51:14 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).
% 4.80/1.11
% 4.80/1.11 % SZS status Unsatisfiable for theBenchmark
% 4.80/1.11
% 4.80/1.11 % Proof 1 at 0.54 (+ 0.17) seconds.
% 4.80/1.11 % Length of proof is 30.
% 4.80/1.11 % Level of proof is 5.
% 4.80/1.11 % Maximum clause weight is 20.000.
% 4.80/1.11 % Given clauses 64.
% 4.80/1.11
% 4.80/1.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------