%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO010+1 : 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 : n018.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 0.15s 5.60s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 184 ( 12 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 201 ( 60 ~; 67 |; 64 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 101 ( 4 sgn 55 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_02,axiom,
! [X4,X5,X6] :
( ( occurrence_of(X4,X6)
& occurrence_of(X4,X5) )
=> X5 = X6 ),
file('theBenchmark.p',sos_02) ).
fof(sos_21,axiom,
! [X56,X57] :
( leaf(X56,X57)
<=> ( ~ ? [X59] : min_precedes(X56,X59,X57)
& ( ? [X58] : min_precedes(X58,X56,X57)
| root(X56,X57) ) ) ),
file('theBenchmark.p',sos_21) ).
fof(sos_34,axiom,
! [X102,X103] :
( leaf_occ(X102,X103)
<=> ? [X104] :
( leaf(X102,X104)
& subactivity_occurrence(X102,X103)
& occurrence_of(X103,X104) ) ),
file('theBenchmark.p',sos_34) ).
fof(sos_35,axiom,
! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107,X108] :
( leaf_occ(X108,X105)
& next_subocc(X107,X108,tptp0)
& ( occurrence_of(X108,tptp2)
| occurrence_of(X108,tptp1) )
& next_subocc(X106,X107,tptp0)
& occurrence_of(X107,tptp4)
& root_occ(X106,X105)
& occurrence_of(X106,tptp3) ) ),
file('theBenchmark.p',sos_35) ).
fof(goals,conjecture,
! [X109] :
( occurrence_of(X109,tptp0)
=> ? [X110,X111] :
( ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( min_precedes(X110,X113,tptp0)
& occurrence_of(X113,tptp1) ) )
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( min_precedes(X110,X112,tptp0)
& occurrence_of(X112,tptp2) ) )
& leaf_occ(X111,X109) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X109] :
( occurrence_of(X109,tptp0)
=> ? [X110,X111] :
( ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( min_precedes(X110,X113,tptp0)
& occurrence_of(X113,tptp1) ) )
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( min_precedes(X110,X112,tptp0)
& occurrence_of(X112,tptp2) ) )
& leaf_occ(X111,X109) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_35,plain,
! [X102,X103] :
( ( ! [X104] :
( ~ leaf(X102,X104)
| ~ subactivity_occurrence(X102,X103)
| ~ occurrence_of(X103,X104) )
| leaf_occ(X102,X103) )
& ( ? [X114] :
( leaf(X102,X114)
& subactivity_occurrence(X102,X103)
& occurrence_of(X103,X114) )
| ~ leaf_occ(X102,X103) ) ),
inference(fof_nnf,[status(thm)],[sos_34]) ).
fof(sk_sos_34_sk,plain,
! [X102,X103] :
( ( ! [X104] :
( ~ leaf(X102,X104)
| ~ subactivity_occurrence(X102,X103)
| ~ occurrence_of(X103,X104) )
| leaf_occ(X102,X103) )
& ( ( leaf(X102,sK0(X102,X103))
& subactivity_occurrence(X102,X103)
& occurrence_of(X103,sK0(X102,X103)) )
| ~ leaf_occ(X102,X103) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X114,sK0(X102,X103))],[nnf_35]) ).
fof(sk_sos_34,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ leaf(VAR_0,VAR_2)
| ~ subactivity_occurrence(VAR_0,VAR_1)
| ~ occurrence_of(VAR_1,VAR_2)
| leaf_occ(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( leaf(VAR_0,sK0(VAR_0,VAR_1))
| ~ leaf_occ(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( subactivity_occurrence(VAR_0,VAR_1)
| ~ leaf_occ(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(VAR_1,sK0(VAR_0,VAR_1))
| ~ leaf_occ(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_34_sk]) ).
cnf(c_95,plain,
( leaf(A,sK0(A,B))
| ~ leaf_occ(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_34]) ).
cnf(c_97,plain,
( ~ min_precedes(A,C,B)
| ~ leaf(A,B) ),
inference(clausify,[status(thm)],[sos_21]) ).
fof(nnf_37,plain,
? [X109] :
( ! [X110,X111] :
( ( ? [X113] :
( min_precedes(X110,X113,tptp0)
& occurrence_of(X113,tptp1) )
& occurrence_of(X111,tptp2) )
| ( ? [X112] :
( min_precedes(X110,X112,tptp0)
& occurrence_of(X112,tptp2) )
& occurrence_of(X111,tptp1) )
| ~ leaf_occ(X111,X109) )
& occurrence_of(X109,tptp0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X110,X111] :
( ( min_precedes(X110,sK3(X110,X111),tptp0)
& occurrence_of(sK3(X110,X111),tptp1)
& occurrence_of(X111,tptp2) )
| ( min_precedes(X110,sK2(X110,X111),tptp0)
& occurrence_of(sK2(X110,X111),tptp2)
& occurrence_of(X111,tptp1) )
| ~ leaf_occ(X111,sK1) )
& occurrence_of(sK1,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X109,sK1),skolemize(X112,sK2(X110,X111)),skolemize(X113,sK3(X110,X111))],[nnf_37]) ).
fof(sk_goals_neg,plain,
( ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK3(VAR_1,VAR_0),tptp0)
| min_precedes(VAR_1,sK2(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK3(VAR_1,VAR_0),tptp1)
| min_precedes(VAR_1,sK2(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(VAR_0,tptp2)
| min_precedes(VAR_1,sK2(VAR_1,VAR_0),tptp0)
| ~ leaf_occ(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK3(VAR_1,VAR_0),tptp0)
| occurrence_of(sK2(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK3(VAR_1,VAR_0),tptp1)
| occurrence_of(sK2(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(VAR_0,tptp2)
| occurrence_of(sK2(VAR_1,VAR_0),tptp2)
| ~ leaf_occ(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( min_precedes(VAR_1,sK3(VAR_1,VAR_0),tptp0)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( occurrence_of(sK3(VAR_1,VAR_0),tptp1)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK1) )
& ! [VAR_0] :
( occurrence_of(VAR_0,tptp2)
| occurrence_of(VAR_0,tptp1)
| ~ leaf_occ(VAR_0,sK1) )
& occurrence_of(sK1,tptp0) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_169,negated_conjecture,
( occurrence_of(A,tptp2)
| min_precedes(B,sK2(B,A),tptp0)
| ~ leaf_occ(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_173,negated_conjecture,
( min_precedes(B,sK3(B,A),tptp0)
| occurrence_of(A,tptp1)
| ~ leaf_occ(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_176,negated_conjecture,
occurrence_of(sK1,tptp0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
fof(sos_47,axiom,
tptp1 != tptp2,
file('theBenchmark.p',sos_47) ).
cnf(c_177,plain,
tptp1 != tptp2,
inference(clausify,[status(thm)],[sos_47]) ).
cnf(c_178,plain,
tptp2 != tptp1,
inference(copy,[status(thm)],[c_177]) ).
fof(nnf_36,plain,
! [X105] :
( ? [X106,X107,X108] :
( leaf_occ(X108,X105)
& next_subocc(X107,X108,tptp0)
& ( occurrence_of(X108,tptp2)
| occurrence_of(X108,tptp1) )
& next_subocc(X106,X107,tptp0)
& occurrence_of(X107,tptp4)
& root_occ(X106,X105)
& occurrence_of(X106,tptp3) )
| ~ occurrence_of(X105,tptp0) ),
inference(fof_nnf,[status(thm)],[sos_35]) ).
fof(sk_sos_35_sk,plain,
! [X105] :
( ( leaf_occ(sK4(X105),X105)
& next_subocc(sK8(X105),sK4(X105),tptp0)
& ( occurrence_of(sK4(X105),tptp2)
| occurrence_of(sK4(X105),tptp1) )
& next_subocc(sK7(X105),sK8(X105),tptp0)
& occurrence_of(sK8(X105),tptp4)
& root_occ(sK7(X105),X105)
& occurrence_of(sK7(X105),tptp3) )
| ~ occurrence_of(X105,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK4]),skolemize(X106,sK7(X105)),skolemize(X107,sK8(X105)),skolemize(X108,sK4(X105))],[nnf_36]) ).
fof(sk_sos_35,plain,
( ! [VAR_0] :
( leaf_occ(sK4(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( next_subocc(sK8(VAR_0),sK4(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK4(VAR_0),tptp2)
| occurrence_of(sK4(VAR_0),tptp1)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( next_subocc(sK7(VAR_0),sK8(VAR_0),tptp0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK8(VAR_0),tptp4)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( root_occ(sK7(VAR_0),VAR_0)
| ~ occurrence_of(VAR_0,tptp0) )
& ! [VAR_0] :
( occurrence_of(sK7(VAR_0),tptp3)
| ~ occurrence_of(VAR_0,tptp0) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos_35_sk]) ).
cnf(c_189,plain,
( leaf_occ(sK4(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_35]) ).
cnf(c_195,plain,
( occurrence_of(B,sK0(A,B))
| ~ leaf_occ(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos_34]) ).
cnf(c_218,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_247,plain,
( ~ leaf_occ(A,C)
| ~ min_precedes(A,B,sK0(A,C)) ),
inference(resolve,[status(thm)],[c_97,c_95]) ).
cnf(c_291,plain,
leaf_occ(sK4(sK1),sK1),
inference(resolve,[status(thm)],[c_189,c_176]) ).
cnf(c_1318,negated_conjecture,
( A = tptp0
| ~ occurrence_of(sK1,A) ),
inference(resolve,[status(thm)],[c_218,c_176]) ).
cnf(c_298,negated_conjecture,
( tptp0 = A
| ~ occurrence_of(sK1,A) ),
inference(copy,[status(thm)],[c_1318]) ).
cnf(c_330,plain,
occurrence_of(sK1,sK0(sK4(sK1),sK1)),
inference(resolve,[status(thm)],[c_291,c_195]) ).
cnf(c_333,plain,
( min_precedes(A,sK3(A,sK4(sK1)),tptp0)
| occurrence_of(sK4(sK1),tptp1) ),
inference(resolve,[status(thm)],[c_291,c_173]) ).
cnf(c_337,plain,
( occurrence_of(sK4(sK1),tptp2)
| min_precedes(A,sK2(A,sK4(sK1)),tptp0) ),
inference(resolve,[status(thm)],[c_291,c_169]) ).
cnf(c_1319,plain,
tptp0 = sK0(sK4(sK1),sK1),
inference(resolve,[status(thm)],[c_330,c_298]) ).
cnf(c_607,plain,
sK0(sK4(sK1),sK1) = tptp0,
inference(copy,[status(thm)],[c_1319]) ).
cnf(c_1320,plain,
( ~ leaf_occ(sK4(sK1),sK1)
| ~ min_precedes(sK4(sK1),A,tptp0) ),
inference(paramod,[status(thm)],[c_607,c_247]) ).
cnf(c_650,plain,
~ min_precedes(sK4(sK1),A,tptp0),
inference(resolve,[status(thm)],[c_291,c_1320]) ).
cnf(c_1148,plain,
occurrence_of(sK4(sK1),tptp1),
inference(resolve,[status(thm)],[c_333,c_650]) ).
cnf(c_1156,plain,
( tptp1 = A
| ~ occurrence_of(sK4(sK1),A) ),
inference(resolve,[status(thm)],[c_1148,c_218]) ).
cnf(c_1316,plain,
occurrence_of(sK4(sK1),tptp2),
inference(resolve,[status(thm)],[c_337,c_650]) ).
cnf(c_1321,plain,
tptp1 = tptp2,
inference(resolve,[status(thm)],[c_1316,c_1156]) ).
cnf(c_1322,plain,
tptp2 = tptp1,
inference(copy,[status(thm)],[c_1321]) ).
cnf(c_1317,plain,
$false,
inference(resolve,[status(thm)],[c_178,c_1322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO010+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n018.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 05:00:11 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3763096 was started by sandbox on n018,
% 0.10/5.38 % Sat Sep 26 05:00:11 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.60
% 0.15/5.60 % SZS status Theorem for theBenchmark
% 0.15/5.60
% 0.15/5.60 % Proof 1 at 0.15 (+ 0.05) seconds.
% 0.15/5.60 % Length of proof is 27.
% 0.15/5.60 % Level of proof is 8.
% 0.15/5.60 % Maximum clause weight is 12.000.
% 0.15/5.60 % Given clauses 343.
% 0.15/5.60
% 0.15/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------