%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG006-1 : 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 : n026.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 08:26:18 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(product_lemma1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( product(VAR_0,additive_inverse(VAR_1),additive_inverse(VAR_2))
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_lemma1) ).
cnf(c_18,plain,
( product(A,additive_inverse(B),additive_inverse(C))
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_lemma1]) ).
fof(b_plus_inverse_c,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('theBenchmark.p',b_plus_inverse_c) ).
cnf(c_21,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(clausify,[status(thm)],[b_plus_inverse_c]) ).
fof(a_times_b,axiom,
product(a,b,aPb),
file('theBenchmark.p',a_times_b) ).
cnf(c_22,plain,
product(a,b,aPb),
inference(clausify,[status(thm)],[a_times_b]) ).
fof(a_times_c,axiom,
product(a,c,aPc),
file('theBenchmark.p',a_times_c) ).
cnf(c_23,plain,
product(a,c,aPc),
inference(clausify,[status(thm)],[a_times_c]) ).
fof(aPb_plus_IaPc,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('theBenchmark.p',aPb_plus_IaPc) ).
cnf(c_24,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(clausify,[status(thm)],[aPb_plus_IaPc]) ).
fof(prove_a_times_bS_Ic_is_aPb_S__IaPc,axiom,
~ product(a,bS_Ic,aPb_S_IaPc),
file('theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
cnf(c_25,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(clausify,[status(thm)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(c_186,plain,
product(a,additive_inverse(c),additive_inverse(aPc)),
inference(resolve,[status(thm)],[c_18,c_23]) ).
cnf(c_246,plain,
( product(a,C,D)
| ~ sum(aPb,B,D)
| ~ sum(b,A,C)
| ~ product(a,A,B) ),
inference(resolve,[status(thm)],[c_13,c_22]) ).
cnf(c_247,plain,
( product(a,bS_Ic,B)
| ~ sum(aPb,A,B)
| ~ product(a,additive_inverse(c),A) ),
inference(resolve,[status(thm)],[c_246,c_21]) ).
cnf(c_248,plain,
( product(a,bS_Ic,aPb_S_IaPc)
| ~ product(a,additive_inverse(c),additive_inverse(aPc)) ),
inference(resolve,[status(thm)],[c_247,c_24]) ).
cnf(c_244,plain,
~ product(a,additive_inverse(c),additive_inverse(aPc)),
inference(resolve,[status(thm)],[c_248,c_25]) ).
cnf(c_245,plain,
$false,
inference(resolve,[status(thm)],[c_244,c_186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:46:55 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 216657 was started by sandbox on n026,
% 0.10/0.37 % Sat Sep 26 05:46:55 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.41
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.41
% 0.10/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.41 % Length of proof is 10.
% 0.10/0.41 % Level of proof is 2.
% 0.10/0.41 % Maximum clause weight is 20.000.
% 0.10/0.41 % Given clauses 25.
% 0.10/0.41
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------