%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO012+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:20:57 AM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 132 ( 8 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 157 ( 59 ~; 56 |; 37 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 53 ( 0 sgn 28 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos,axiom,
! [X0,X1,X2,X3] :
( ( min_precedes(X1,X2,X3)
& min_precedes(X0,X1,X3) )
=> min_precedes(X0,X2,X3) ),
file('theBenchmark.p',sos) ).
fof(sos_32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97,X98] :
( ! [X99] :
( min_precedes(X96,X99,tptp0)
=> ( X99 = X98
| X99 = X97 ) )
& min_precedes(X97,X98,tptp0)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) )
& min_precedes(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) ) ),
file('theBenchmark.p',sos_32) ).
fof(goals,conjecture,
! [X100] :
( occurrence_of(X100,tptp0)
=> ? [X101,X102] :
( min_precedes(X101,X102,tptp0)
& ( occurrence_of(X102,tptp1)
| occurrence_of(X102,tptp2) )
& root_occ(X101,X100)
& occurrence_of(X101,tptp3) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X100] :
( occurrence_of(X100,tptp0)
=> ? [X101,X102] :
( min_precedes(X101,X102,tptp0)
& ( occurrence_of(X102,tptp1)
| occurrence_of(X102,tptp2) )
& root_occ(X101,X100)
& occurrence_of(X101,tptp3) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_34,plain,
? [X100] :
( ! [X101,X102] :
( ~ min_precedes(X101,X102,tptp0)
| ( ~ occurrence_of(X102,tptp1)
& ~ occurrence_of(X102,tptp2) )
| ~ root_occ(X101,X100)
| ~ occurrence_of(X101,tptp3) )
& occurrence_of(X100,tptp0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X101,X102] :
( ~ min_precedes(X101,X102,tptp0)
| ( ~ occurrence_of(X102,tptp1)
& ~ occurrence_of(X102,tptp2) )
| ~ root_occ(X101,sK0)
| ~ occurrence_of(X101,tptp3) )
& occurrence_of(sK0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X100,sK0)],[nnf_34]) ).
fof(sk_goals_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ min_precedes(VAR_0,VAR_1,tptp0)
| ~ occurrence_of(VAR_1,tptp1)
| ~ root_occ(VAR_0,sK0)
| ~ occurrence_of(VAR_0,tptp3) )
& ! [VAR_0,VAR_1] :
( ~ min_precedes(VAR_0,VAR_1,tptp0)
| ~ occurrence_of(VAR_1,tptp2)
| ~ root_occ(VAR_0,sK0)
| ~ occurrence_of(VAR_0,tptp3) )
& occurrence_of(sK0,tptp0) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_116,negated_conjecture,
( ~ min_precedes(A,B,tptp0)
| ~ occurrence_of(B,tptp1)
| ~ root_occ(A,sK0)
| ~ occurrence_of(A,tptp3) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_117,negated_conjecture,
( ~ min_precedes(A,B,tptp0)
| ~ occurrence_of(B,tptp2)
| ~ root_occ(A,sK0)
| ~ occurrence_of(A,tptp3) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_118,negated_conjecture,
occurrence_of(sK0,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
fof(nnf_33,plain,
! [X95] :
( ? [X96,X97,X98] :
( ! [X99] :
( X99 = X98
| X99 = X97
| ~ min_precedes(X96,X99,tptp0) )
& min_precedes(X97,X98,tptp0)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) )
& min_precedes(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_32]) ).
fof(sk_sos_32_sk,plain,
! [X95] :
( ( ! [X99] :
( X99 = sK2(X95)
| X99 = sK1(X95)
| ~ min_precedes(sK3(X95),X99,tptp0) )
& min_precedes(sK1(X95),sK2(X95),tptp0)
& ( occurrence_of(sK2(X95),tptp1)
| occurrence_of(sK2(X95),tptp2) )
& min_precedes(sK3(X95),sK1(X95),tptp0)
& occurrence_of(sK1(X95),tptp4)
& root_occ(sK3(X95),X95)
& occurrence_of(sK3(X95),tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2]),skolemize(X96,sK3(X95)),skolemize(X97,sK1(X95)),skolemize(X98,sK2(X95))],[nnf_33]) ).
fof(sk_sos_32,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 = sK2(VAR_0)
| VAR_1 = sK1(VAR_0)
| ~ min_precedes(sK3(VAR_0),VAR_1,tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( min_precedes(sK1(VAR_0),sK2(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK2(VAR_0),tptp1)
| occurrence_of(sK2(VAR_0),tptp2)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( min_precedes(sK3(VAR_0),sK1(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK1(VAR_0),tptp4)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( root_occ(sK3(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK3(VAR_0),tptp3)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_32_sk]) ).
cnf(c_132,plain,
( min_precedes(sK1(A),sK2(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_133,plain,
( occurrence_of(sK2(A),tptp1)
| occurrence_of(sK2(A),tptp2)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_134,plain,
( min_precedes(sK3(A),sK1(A),tptp0)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_136,plain,
( root_occ(sK3(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_137,plain,
( occurrence_of(sK3(A),tptp3)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_168,plain,
( min_precedes(A,D,C)
| ~ min_precedes(B,D,C)
| ~ min_precedes(A,B,C) ),
inference(clausify,[status(thm)],[sos]) ).
cnf(c_205,plain,
min_precedes(sK1(sK0),sK2(sK0),tptp0),
inference(resolve,[status(thm)],[c_132,c_118]) ).
cnf(c_206,plain,
( occurrence_of(sK2(sK0),tptp1)
| occurrence_of(sK2(sK0),tptp2) ),
inference(resolve,[status(thm)],[c_133,c_118]) ).
cnf(c_207,plain,
min_precedes(sK3(sK0),sK1(sK0),tptp0),
inference(resolve,[status(thm)],[c_134,c_118]) ).
cnf(c_209,plain,
root_occ(sK3(sK0),sK0),
inference(resolve,[status(thm)],[c_136,c_118]) ).
cnf(c_210,plain,
occurrence_of(sK3(sK0),tptp3),
inference(resolve,[status(thm)],[c_137,c_118]) ).
cnf(c_262,plain,
( min_precedes(A,sK2(sK0),tptp0)
| ~ min_precedes(A,sK1(sK0),tptp0) ),
inference(resolve,[status(thm)],[c_205,c_168]) ).
cnf(c_416,plain,
min_precedes(sK3(sK0),sK2(sK0),tptp0),
inference(resolve,[status(thm)],[c_262,c_207]) ).
cnf(c_437,negated_conjecture,
( ~ occurrence_of(sK2(sK0),tptp2)
| ~ root_occ(sK3(sK0),sK0)
| ~ occurrence_of(sK3(sK0),tptp3) ),
inference(resolve,[status(thm)],[c_416,c_117]) ).
cnf(c_438,negated_conjecture,
( ~ occurrence_of(sK2(sK0),tptp2)
| ~ root_occ(sK3(sK0),sK0) ),
inference(resolve,[status(thm)],[c_210,c_437]) ).
cnf(c_428,negated_conjecture,
~ occurrence_of(sK2(sK0),tptp2),
inference(resolve,[status(thm)],[c_209,c_438]) ).
cnf(c_439,negated_conjecture,
( ~ occurrence_of(sK2(sK0),tptp1)
| ~ root_occ(sK3(sK0),sK0)
| ~ occurrence_of(sK3(sK0),tptp3) ),
inference(resolve,[status(thm)],[c_416,c_116]) ).
cnf(c_440,negated_conjecture,
( ~ occurrence_of(sK2(sK0),tptp1)
| ~ root_occ(sK3(sK0),sK0) ),
inference(resolve,[status(thm)],[c_210,c_439]) ).
cnf(c_429,negated_conjecture,
~ occurrence_of(sK2(sK0),tptp1),
inference(resolve,[status(thm)],[c_209,c_440]) ).
cnf(c_441,plain,
occurrence_of(sK2(sK0),tptp1),
inference(resolve,[status(thm)],[c_428,c_206]) ).
cnf(c_436,plain,
$false,
inference(resolve,[status(thm)],[c_429,c_441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PRO012+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 04:58:16 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1237894 was started by sandbox2 on n005,
% 0.16/0.43 % Sat Sep 26 04:58:16 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.50
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50
% 0.16/0.50 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/0.50 % Length of proof is 22.
% 0.16/0.50 % Level of proof is 6.
% 0.16/0.50 % Maximum clause weight is 21.000.
% 0.16/0.50 % Given clauses 169.
% 0.16/0.50
% 0.16/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------