%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PRO010+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 : n007.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 0.11s 0.42s
% Output : CNFRefutation 0.11s
% 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_21,axiom,
! [X60,X61,X62] :
( ( leaf_occ(X61,X60)
& occurrence_of(X60,X62) )
=> ~ ? [X63] : min_precedes(X61,X63,X62) ),
file('theBenchmark.p',sos_21) ).
fof(sos_22,axiom,
! [X64,X65,X66] :
( ( occurrence_of(X64,X66)
& occurrence_of(X64,X65) )
=> X65 = X66 ),
file('theBenchmark.p',sos_22) ).
fof(sos_32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& next_subocc(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) ) ),
file('theBenchmark.p',sos_32) ).
fof(goals,conjecture,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) ) )
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) ) )
& leaf_occ(X101,X99) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) ) )
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) ) )
& leaf_occ(X101,X99) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_34,plain,
? [X99] :
( ! [X100,X101] :
( ( ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) )
& occurrence_of(X101,tptp2) )
| ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) )
& occurrence_of(X101,tptp1) )
| ~ leaf_occ(X101,X99) )
& occurrence_of(X99,tptp0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ! [X100,X101] :
( ( min_precedes(X100,sK2(X100,X101),tptp0)
& occurrence_of(sK2(X100,X101),tptp1)
& occurrence_of(X101,tptp2) )
| ( min_precedes(X100,sK1(X100,X101),tptp0)
& occurrence_of(sK1(X100,X101),tptp2)
& occurrence_of(X101,tptp1) )
| ~ leaf_occ(X101,sK0) )
& occurrence_of(sK0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X99,sK0),skolemize(X102,sK1(X100,X101)),skolemize(X103,sK2(X100,X101))],[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_127,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_131,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_134,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_135,plain,
tptp1 != tptp2,
inference(clausify,[status(thm)],[sos_44]) ).
cnf(c_136,plain,
tptp2 != tptp1,
inference(copy,[status(thm)],[c_135]) ).
fof(nnf_33,plain,
! [X95] :
( ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& next_subocc(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] :
( ( leaf_occ(sK3(X95),X95)
& next_subocc(sK5(X95),sK3(X95),tptp0)
& ( occurrence_of(sK3(X95),tptp2)
| occurrence_of(sK3(X95),tptp1) )
& next_subocc(sK4(X95),sK5(X95),tptp0)
& occurrence_of(sK5(X95),tptp4)
& root_occ(sK4(X95),X95)
& occurrence_of(sK4(X95),tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK3]),skolemize(X96,sK4(X95)),skolemize(X97,sK5(X95)),skolemize(X98,sK3(X95))],[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_147,plain,
( leaf_occ(sK3(A),A)
| ~ occurrence_of(A,tptp0) ),
inference(split_conjunct,[status(thm)],[sk_sos_32]) ).
cnf(c_163,plain,
( C = B
| ~ occurrence_of(A,C)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_22]) ).
cnf(c_164,plain,
( ~ min_precedes(C,D,B)
| ~ leaf_occ(C,A)
| ~ occurrence_of(A,B) ),
inference(clausify,[status(thm)],[sos_21]) ).
cnf(c_224,plain,
leaf_occ(sK3(sK0),sK0),
inference(resolve,[status(thm)],[c_147,c_134]) ).
cnf(c_269,plain,
( min_precedes(A,sK2(A,sK3(sK0)),tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_224,c_131]) ).
cnf(c_273,plain,
( occurrence_of(sK3(sK0),tptp2)
| min_precedes(A,sK1(A,sK3(sK0)),tptp0) ),
inference(resolve,[status(thm)],[c_224,c_127]) ).
cnf(c_611,plain,
( ~ leaf_occ(B,A)
| ~ occurrence_of(A,tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_269,c_164]) ).
cnf(c_744,plain,
( ~ occurrence_of(sK0,tptp0)
| occurrence_of(sK3(sK0),tptp1) ),
inference(resolve,[status(thm)],[c_611,c_224]) ).
cnf(c_686,negated_conjecture,
occurrence_of(sK3(sK0),tptp1),
inference(resolve,[status(thm)],[c_134,c_744]) ).
cnf(c_688,plain,
( tptp1 = A
| ~ occurrence_of(sK3(sK0),A) ),
inference(resolve,[status(thm)],[c_686,c_163]) ).
cnf(c_720,plain,
( ~ leaf_occ(B,A)
| ~ occurrence_of(A,tptp0)
| occurrence_of(sK3(sK0),tptp2) ),
inference(resolve,[status(thm)],[c_273,c_164]) ).
cnf(c_745,plain,
( ~ occurrence_of(sK0,tptp0)
| occurrence_of(sK3(sK0),tptp2) ),
inference(resolve,[status(thm)],[c_720,c_224]) ).
cnf(c_742,negated_conjecture,
occurrence_of(sK3(sK0),tptp2),
inference(resolve,[status(thm)],[c_134,c_745]) ).
cnf(c_746,plain,
tptp1 = tptp2,
inference(resolve,[status(thm)],[c_742,c_688]) ).
cnf(c_747,plain,
tptp2 = tptp1,
inference(copy,[status(thm)],[c_746]) ).
cnf(c_743,plain,
$false,
inference(resolve,[status(thm)],[c_136,c_747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n007.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 04:55:54 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 2825214 was started by sandbox2 on n007,
% 0.07/0.34 % Sat Sep 26 04:55:54 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.11/0.42
% 0.11/0.42 % SZS status Theorem for theBenchmark
% 0.11/0.42
% 0.11/0.42 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.11/0.42 % Length of proof is 21.
% 0.11/0.42 % Level of proof is 7.
% 0.11/0.42 % Maximum clause weight is 26.000.
% 0.11/0.42 % Given clauses 248.
% 0.11/0.42
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------