%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO011+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 : n011.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 0.73s 0.50s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 177 ( 8 equ)
% Maximal formula atoms : 49 ( 5 avg)
% Number of connectives : 195 ( 51 ~; 67 |; 68 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 90 ( 3 sgn 53 !; 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)
& subactivity_occurrence(X109,X105)
& occurrence_of(X109,tptp1) ) )
& ( occurrence_of(X107,tptp1)
=> ~ ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& 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)
& subactivity_occurrence(X109,X105)
& occurrence_of(X109,tptp1) ) )
& ( occurrence_of(X107,tptp1)
=> ~ ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& 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)
& subactivity_occurrence(X109,X105)
& occurrence_of(X109,tptp1) )
& occurrence_of(X107,tptp2) )
| ( ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& 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)
& subactivity_occurrence(sK2(X106,X107),sK0)
& occurrence_of(sK2(X106,X107),tptp1)
& occurrence_of(X107,tptp2) )
| ( min_precedes(X106,sK1(X106,X107),tptp0)
& subactivity_occurrence(sK1(X106,X107),sK0)
& 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] :
( subactivity_occurrence(sK2(VAR_1,VAR_0),sK0)
| 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)
| subactivity_occurrence(sK1(VAR_1,VAR_0),sK0)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( subactivity_occurrence(sK2(VAR_1,VAR_0),sK0)
| subactivity_occurrence(sK1(VAR_1,VAR_0),sK0)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK2(VAR_1,VAR_0),tptp1)
| subactivity_occurrence(sK1(VAR_1,VAR_0),sK0)
| ~ leaf_occ(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( occurrence_of(VAR_0,tptp2)
| subactivity_occurrence(sK1(VAR_1,VAR_0),sK0)
| ~ 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] :
( subactivity_occurrence(sK2(VAR_1,VAR_0),sK0)
| 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] :
( subactivity_occurrence(sK2(VAR_1,VAR_0),sK0)
| 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_151,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_160,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_164,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_165,plain,
tptp1 != tptp2,
inference(clausify,[status(thm)],[sos_44]) ).
cnf(c_166,plain,
tptp2 != tptp1,
inference(copy,[status(thm)],[c_165]) ).
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_177,plain,
( leaf_occ(sK3(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_200,plain,
( ~ min_precedes(C,D,B)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_201,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_245,plain,
leaf_occ(sK3(sK0),sK0),
inference(resolve,[status(thm)],[c_177,c_164]) ).
cnf(c_273,plain,
( min_precedes(A,sK2(A,sK3(sK0)),tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_245,c_160]) ).
cnf(c_282,plain,
( occurrence_of(sK3(sK0),tptp2)
| min_precedes(A,sK1(A,sK3(sK0)),tptp0) ),
inference(resolve,[status(thm)],[c_245,c_151]) ).
cnf(c_719,plain,
( ~ leaf_occ(B,A)
| ~ occurrence_of(A,tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_273,c_200]) ).
cnf(c_821,plain,
( ~ occurrence_of(sK0,tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_719,c_245]) ).
cnf(c_757,negated_conjecture,
occurrence_of(sK3(sK0),tptp1),
inference(resolve,[status(thm)],[c_164,c_821]) ).
cnf(c_758,plain,
( tptp1 = A
| ~ occurrence_of(sK3(sK0),A) ),
inference(resolve,[status(thm)],[c_757,c_201]) ).
cnf(c_787,plain,
( ~ leaf_occ(B,A)
| ~ occurrence_of(A,tptp0)
| occurrence_of(sK3(sK0),tptp2) ),
inference(resolve,[status(thm)],[c_282,c_200]) ).
cnf(c_822,plain,
( ~ occurrence_of(sK0,tptp0)
| occurrence_of(sK3(sK0),tptp2) ),
inference(resolve,[status(thm)],[c_787,c_245]) ).
cnf(c_819,negated_conjecture,
occurrence_of(sK3(sK0),tptp2),
inference(resolve,[status(thm)],[c_164,c_822]) ).
cnf(c_823,plain,
tptp1 = tptp2,
inference(resolve,[status(thm)],[c_819,c_758]) ).
cnf(c_824,plain,
tptp2 = tptp1,
inference(copy,[status(thm)],[c_823]) ).
cnf(c_820,plain,
$false,
inference(resolve,[status(thm)],[c_166,c_824]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO011+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.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 04:58:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3812818 was started by sandbox on n011,
% 0.09/0.37 % Sat Sep 26 04:58:44 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.73/0.50
% 0.73/0.50 % SZS status Theorem for theBenchmark
% 0.73/0.50
% 0.73/0.50 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.73/0.50 % Length of proof is 21.
% 0.73/0.50 % Level of proof is 7.
% 0.73/0.50 % Maximum clause weight is 26.000.
% 0.73/0.50 % Given clauses 241.
% 0.73/0.50
% 0.73/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------