%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO010+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:20:56 AM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 148 ( 8 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 159 ( 44 ~; 53 |; 53 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 76 ( 3 sgn 39 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_08,axiom,
! [X28,X29,X30] :
( ( occurrence_of(X28,X30)
& occurrence_of(X28,X29) )
=> X29 = X30 ),
file('theBenchmark.p',sos_08) ).
fof(sos_09,axiom,
! [X31,X32,X33] :
( ( leaf_occ(X32,X31)
& occurrence_of(X31,X33) )
=> ~ ? [X34] : min_precedes(X32,X34,X33) ),
file('theBenchmark.p',sos_09) ).
fof(sos_32,axiom,
! [X101] :
( occurrence_of(X101,tptp0)
=> ? [X102,X103,X104] :
( leaf_occ(X104,X101)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp2)
| occurrence_of(X104,tptp1) )
& next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) ) ),
file('theBenchmark.p',sos_32) ).
fof(goals,conjecture,
! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107] :
( ( occurrence_of(X107,tptp2)
=> ~ ? [X109] :
( min_precedes(X106,X109,tptp0)
& occurrence_of(X109,tptp1) ) )
& ( occurrence_of(X107,tptp1)
=> ~ ? [X108] :
( min_precedes(X106,X108,tptp0)
& occurrence_of(X108,tptp2) ) )
& leaf_occ(X107,X105) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107] :
( ( occurrence_of(X107,tptp2)
=> ~ ? [X109] :
( min_precedes(X106,X109,tptp0)
& occurrence_of(X109,tptp1) ) )
& ( occurrence_of(X107,tptp1)
=> ~ ? [X108] :
( min_precedes(X106,X108,tptp0)
& occurrence_of(X108,tptp2) ) )
& leaf_occ(X107,X105) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_34,plain,
? [X105] :
( ! [X106,X107] :
( ( ? [X109] :
( min_precedes(X106,X109,tptp0)
& occurrence_of(X109,tptp1) )
& occurrence_of(X107,tptp2) )
| ( ? [X108] :
( min_precedes(X106,X108,tptp0)
& occurrence_of(X108,tptp2) )
& occurrence_of(X107,tptp1) )
| ~ leaf_occ(X107,X105) )
& occurrence_of(X105,tptp0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X106,X107] :
( ( min_precedes(X106,sK2(X106,X107),tptp0)
& occurrence_of(sK2(X106,X107),tptp1)
& occurrence_of(X107,tptp2) )
| ( min_precedes(X106,sK1(X106,X107),tptp0)
& occurrence_of(sK1(X106,X107),tptp2)
& occurrence_of(X107,tptp1) )
| ~ leaf_occ(X107,sK0) )
& occurrence_of(sK0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X105,sK0),skolemize(X108,sK1(X106,X107)),skolemize(X109,sK2(X106,X107))],[nnf_34]) ).
fof(sk_goals_neg,plain,
( ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK2(VAR_1,VAR_0),tptp0)
| min_precedes(VAR_1,sK1(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK2(VAR_1,VAR_0),tptp1)
| min_precedes(VAR_1,sK1(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(VAR_0,tptp2)
| min_precedes(VAR_1,sK1(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK2(VAR_1,VAR_0),tptp0)
| occurrence_of(sK1(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK2(VAR_1,VAR_0),tptp1)
| occurrence_of(sK1(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(VAR_0,tptp2)
| occurrence_of(sK1(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK2(VAR_1,VAR_0),tptp0)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK2(VAR_1,VAR_0),tptp1)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0] :
( occurrence_of(VAR_0,tptp2)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK0) )
& occurrence_of(sK0,tptp0) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_150,negated_conjecture,
( occurrence_of(A,tptp2)
| min_precedes(B,sK1(B,A),tptp0)
| ~ leaf_occ(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_154,negated_conjecture,
( min_precedes(B,sK2(B,A),tptp0)
| occurrence_of(A,tptp1)
| ~ leaf_occ(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_157,negated_conjecture,
occurrence_of(sK0,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
fof(sos_44,axiom,
tptp1 != tptp2,
file('theBenchmark.p',sos_44) ).
cnf(c_158,plain,
tptp1 != tptp2,
inference(clausify,[status(thm)],[sos_44]) ).
cnf(c_159,plain,
tptp2 != tptp1,
inference(copy,[status(thm)],[c_158]) ).
fof(nnf_33,plain,
! [X101] :
( ? [X102,X103,X104] :
( leaf_occ(X104,X101)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp2)
| occurrence_of(X104,tptp1) )
& next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_32]) ).
fof(sk_sos_32_sk,plain,
! [X101] :
( ( leaf_occ(sK3(X101),X101)
& next_subocc(sK5(X101),sK3(X101),tptp0)
& ( occurrence_of(sK3(X101),tptp2)
| occurrence_of(sK3(X101),tptp1) )
& next_subocc(sK4(X101),sK5(X101),tptp0)
& occurrence_of(sK5(X101),tptp4)
& root_occ(sK4(X101),X101)
& occurrence_of(sK4(X101),tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK3]),skolemize(X102,sK4(X101)),skolemize(X103,sK5(X101)),skolemize(X104,sK3(X101))],[nnf_33]) ).
fof(sk_sos_32,plain,
( ! [VAR_0] :
( leaf_occ(sK3(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( next_subocc(sK5(VAR_0),sK3(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK3(VAR_0),tptp2)
| occurrence_of(sK3(VAR_0),tptp1)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( next_subocc(sK4(VAR_0),sK5(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK5(VAR_0),tptp4)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( root_occ(sK4(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK4(VAR_0),tptp3)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_32_sk]) ).
cnf(c_170,plain,
( leaf_occ(sK3(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_193,plain,
( ~ min_precedes(C,D,B)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_194,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_238,plain,
leaf_occ(sK3(sK0),sK0),
inference(resolve,[status(thm)],[c_170,c_157]) ).
cnf(c_308,plain,
( min_precedes(A,sK2(A,sK3(sK0)),tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_238,c_154]) ).
cnf(c_312,plain,
( occurrence_of(sK3(sK0),tptp2)
| min_precedes(A,sK1(A,sK3(sK0)),tptp0) ),
inference(resolve,[status(thm)],[c_238,c_150]) ).
cnf(c_768,plain,
( ~ leaf_occ(B,A)
| ~ occurrence_of(A,tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_308,c_193]) ).
cnf(c_912,plain,
( ~ occurrence_of(sK0,tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_768,c_238]) ).
cnf(c_797,negated_conjecture,
occurrence_of(sK3(sK0),tptp1),
inference(resolve,[status(thm)],[c_157,c_912]) ).
cnf(c_798,plain,
( tptp1 = A
| ~ occurrence_of(sK3(sK0),A) ),
inference(resolve,[status(thm)],[c_797,c_194]) ).
cnf(c_822,plain,
( ~ leaf_occ(B,A)
| ~ occurrence_of(A,tptp0)
| occurrence_of(sK3(sK0),tptp2) ),
inference(resolve,[status(thm)],[c_312,c_193]) ).
cnf(c_913,plain,
( ~ occurrence_of(sK0,tptp0)
| occurrence_of(sK3(sK0),tptp2) ),
inference(resolve,[status(thm)],[c_822,c_238]) ).
cnf(c_910,negated_conjecture,
occurrence_of(sK3(sK0),tptp2),
inference(resolve,[status(thm)],[c_157,c_913]) ).
cnf(c_914,plain,
tptp1 = tptp2,
inference(resolve,[status(thm)],[c_910,c_798]) ).
cnf(c_915,plain,
tptp2 = tptp1,
inference(copy,[status(thm)],[c_914]) ).
cnf(c_911,plain,
$false,
inference(resolve,[status(thm)],[c_159,c_915]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PRO010+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 04:58:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 3949264 was started by sandbox on n012,
% 0.03/0.31 % Sat Sep 26 04:58:04 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39
% 0.08/0.39 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.08/0.39 % Length of proof is 21.
% 0.08/0.39 % Level of proof is 7.
% 0.08/0.39 % Maximum clause weight is 26.000.
% 0.08/0.39 % Given clauses 207.
% 0.08/0.39
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------