%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG039-2 : 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 : 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 08:26:28 AM UTC 2026
% Result : Unsatisfiable 135.08s 17.58s
% Output : CNFRefutation 135.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 64 ( 34 ~; 30 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_18,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_19,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_22,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(sum_right_concellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_3,VAR_1)
| ~ sum(VAR_0,VAR_3,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',sum_right_concellation) ).
cnf(c_31,plain,
( equalish(D,B)
| ~ sum(A,D,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[sum_right_concellation]) ).
fof(absorbtion1,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,add(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',absorbtion1) ).
cnf(c_32,plain,
sum(A,add(A,B),B),
inference(clausify,[status(thm)],[absorbtion1]) ).
fof(absorbtion2,axiom,
! [VAR_0,VAR_1] : sum(add(VAR_0,VAR_1),VAR_1,VAR_0),
file('theBenchmark.p',absorbtion2) ).
cnf(c_33,plain,
sum(add(A,B),B,A),
inference(clausify,[status(thm)],[absorbtion2]) ).
fof(clause68,axiom,
product(add(b,a),b,add(b,c)),
file('theBenchmark.p',clause68) ).
cnf(c_68,plain,
product(add(b,a),b,add(b,c)),
inference(clausify,[status(thm)],[clause68]) ).
fof(clause69,axiom,
product(add(b,a),a,add(d,a)),
file('theBenchmark.p',clause69) ).
cnf(c_69,plain,
product(add(b,a),a,add(d,a)),
inference(clausify,[status(thm)],[clause69]) ).
fof(clause71,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',clause71) ).
cnf(c_71,plain,
product(A,A,A),
inference(clausify,[status(thm)],[clause71]) ).
fof(prove_c_equals_d,axiom,
~ equalish(c,d),
file('theBenchmark.p',prove_c_equals_d) ).
cnf(c_74,plain,
~ equalish(c,d),
inference(clausify,[status(thm)],[prove_c_equals_d]) ).
cnf(c_212,plain,
sum(add(A,B),A,B),
inference(resolve,[status(thm)],[c_19,c_32]) ).
cnf(c_21486,plain,
( sum(A,C,E)
| ~ product(A,D,E)
| ~ sum(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_22,c_71]) ).
cnf(c_21487,plain,
( sum(add(b,a),add(d,a),B)
| ~ product(add(b,a),A,B)
| ~ sum(add(b,a),a,A) ),
inference(resolve,[status(thm)],[c_21486,c_69]) ).
cnf(c_21488,plain,
( sum(add(b,a),add(d,a),A)
| ~ product(add(b,a),b,A) ),
inference(resolve,[status(thm)],[c_21487,c_33]) ).
cnf(c_6437,plain,
sum(add(b,a),add(d,a),add(b,c)),
inference(resolve,[status(thm)],[c_21488,c_68]) ).
cnf(c_21489,plain,
( equalish(B,C)
| ~ sum(add(A,B),C,A) ),
inference(resolve,[status(thm)],[c_31,c_33]) ).
cnf(c_7387,plain,
~ sum(add(A,c),d,A),
inference(resolve,[status(thm)],[c_21489,c_74]) ).
cnf(c_21490,plain,
( sum(D,B,E)
| ~ sum(A,C,E)
| ~ sum(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_18,c_212]) ).
cnf(c_21491,plain,
( sum(D,C,A)
| ~ sum(add(A,B),add(C,B),D) ),
inference(resolve,[status(thm)],[c_21490,c_33]) ).
cnf(c_21484,plain,
~ sum(add(A,B),add(d,B),add(A,c)),
inference(resolve,[status(thm)],[c_21491,c_7387]) ).
cnf(c_21485,plain,
$false,
inference(resolve,[status(thm)],[c_21484,c_6437]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n003.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Sep 26 05:53:09 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2172544 was started by sandbox2 on n003,
% 0.12/0.37 % Sat Sep 26 05:53:09 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 135.08/17.58
% 135.08/17.58 % SZS status Unsatisfiable for theBenchmark
% 135.08/17.58
% 135.08/17.58 % Proof 1 at 12.07 (+ 5.06) seconds.
% 135.08/17.58 % Length of proof is 15.
% 135.08/17.58 % Level of proof is 3.
% 135.08/17.58 % Maximum clause weight is 20.000.
% 135.08/17.58 % Given clauses 172.
% 135.08/17.58
% 135.08/17.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------