%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PRO012+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 : Fri Sep 25 02:31:22 PM UTC 2026
% Result : Theorem 276.69s 35.68s
% Output : Proof 276.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 82 ( 23 unt; 0 def)
% Number of atoms : 240 ( 19 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 258 ( 100 ~; 98 |; 50 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 141 ( 1 sgn 71 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [X101] :
( occurrence_of(X101,tptp0)
=> ? [X102,X103,X104] :
( ! [X105] :
( min_precedes(X102,X105,tptp0)
=> ( X105 = X104
| X105 = X103 ) )
& min_precedes(X103,X104,tptp0)
& ( occurrence_of(X104,tptp1)
| occurrence_of(X104,tptp2) )
& min_precedes(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
fof(f32_nnf,plain,
! [X101] :
( ? [X102,X103,X104] :
( ! [X105] :
( X105 = X104
| X105 = X103
| ~ min_precedes(X102,X105,tptp0) )
& min_precedes(X103,X104,tptp0)
& ( occurrence_of(X104,tptp1)
| occurrence_of(X104,tptp2) )
& min_precedes(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X101,X105] :
( ( ( X105 = sk14(X101)
| X105 = sk13(X101)
| ~ min_precedes(sk12(X101),X105,tptp0) )
& min_precedes(sk13(X101),sk14(X101),tptp0)
& ( occurrence_of(sk14(X101),tptp1)
| occurrence_of(sk14(X101),tptp2) )
& min_precedes(sk12(X101),sk13(X101),tptp0)
& occurrence_of(sk13(X101),tptp4)
& root_occ(sk12(X101),X101)
& occurrence_of(sk12(X101),tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13,sk14])],[f32_nnf]) ).
cnf(c65,plain,
( min_precedes(sk13(X0),sk14(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f45,conjecture,
! [X106] :
( occurrence_of(X106,tptp0)
=> ? [X107,X108] :
( min_precedes(X107,X108,tptp0)
& ( occurrence_of(X108,tptp1)
| occurrence_of(X108,tptp2) )
& root_occ(X107,X106)
& occurrence_of(X107,tptp3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f45_neg,negated_conjecture,
~ ! [X106] :
( occurrence_of(X106,tptp0)
=> ? [X107,X108] :
( min_precedes(X107,X108,tptp0)
& ( occurrence_of(X108,tptp1)
| occurrence_of(X108,tptp2) )
& root_occ(X107,X106)
& occurrence_of(X107,tptp3) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f45_nnf,plain,
? [X106] :
( ! [X107,X108] :
( ~ min_precedes(X107,X108,tptp0)
| ( ~ occurrence_of(X108,tptp1)
& ~ occurrence_of(X108,tptp2) )
| ~ root_occ(X107,X106)
| ~ occurrence_of(X107,tptp3) )
& occurrence_of(X106,tptp0) ),
inference(nnf_transformation,[status(thm)],[f45_neg]) ).
fof(f45_sk,plain,
! [X107,X108] :
( ( ~ min_precedes(X107,X108,tptp0)
| ( ~ occurrence_of(X108,tptp1)
& ~ occurrence_of(X108,tptp2) )
| ~ root_occ(X107,sk15)
| ~ occurrence_of(X107,tptp3) )
& occurrence_of(sk15,tptp0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f45_nnf]) ).
cnf(c79,plain,
occurrence_of(sk15,tptp0),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p525,plain,
min_precedes(sk13(sk15),sk14(sk15),tptp0),
inference(resolution,[status(thm)],[c65,c79]) ).
fof(f23,axiom,
! [X68,X69,X70] :
( min_precedes(X68,X69,X70)
=> ? [X71] :
( min_precedes(X71,X69,X70)
& root(X71,X70) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_23) ).
fof(f23_nnf,plain,
! [X68,X69,X70] :
( ? [X71] :
( min_precedes(X71,X69,X70)
& root(X71,X70) )
| ~ min_precedes(X68,X69,X70) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X68,X69,X70] :
( ( min_precedes(sk10(X68,X69,X70),X69,X70)
& root(sk10(X68,X69,X70),X70) )
| ~ min_precedes(X68,X69,X70) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f23_nnf]) ).
cnf(c47,plain,
( min_precedes(sk10(X0,X1,X2),X1,X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p543,plain,
min_precedes(sk10(sk13(sk15),sk14(sk15),tptp0),sk14(sk15),tptp0),
inference(resolution,[status(thm)],[p525,c47]) ).
fof(f27,axiom,
! [X82,X83,X84,X85] :
( ( subactivity_occurrence(X83,X85)
& occurrence_of(X85,X84)
& min_precedes(X82,X83,X84) )
=> subactivity_occurrence(X82,X85) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_27) ).
fof(f27_nnf,plain,
! [X82,X83,X84,X85] :
( subactivity_occurrence(X82,X85)
| ~ subactivity_occurrence(X83,X85)
| ~ occurrence_of(X85,X84)
| ~ min_precedes(X82,X83,X84) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X82,X83,X84,X85] :
( subactivity_occurrence(X82,X85)
| ~ subactivity_occurrence(X83,X85)
| ~ occurrence_of(X85,X84)
| ~ min_precedes(X82,X83,X84) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c55,plain,
( subactivity_occurrence(X0,X3)
| ~ subactivity_occurrence(X1,X3)
| ~ occurrence_of(X3,X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p1079,plain,
( subactivity_occurrence(sk10(sk13(sk15),sk14(sk15),tptp0),X0)
| ~ subactivity_occurrence(sk14(sk15),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[p543,c55]) ).
fof(f6,axiom,
! [X21,X22,X23] :
( min_precedes(X22,X23,X21)
=> ? [X24] :
( subactivity_occurrence(X23,X24)
& subactivity_occurrence(X22,X24)
& occurrence_of(X24,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(f6_nnf,plain,
! [X21,X22,X23] :
( ? [X24] :
( subactivity_occurrence(X23,X24)
& subactivity_occurrence(X22,X24)
& occurrence_of(X24,X21) )
| ~ min_precedes(X22,X23,X21) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X22,X23,X21] :
( ( subactivity_occurrence(X23,sk2(X21,X22,X23))
& subactivity_occurrence(X22,sk2(X21,X22,X23))
& occurrence_of(sk2(X21,X22,X23),X21) )
| ~ min_precedes(X22,X23,X21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f6_nnf]) ).
cnf(c9,plain,
( occurrence_of(sk2(X0,X1,X2),X0)
| ~ min_precedes(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p537,plain,
occurrence_of(sk2(tptp0,sk13(sk15),sk14(sk15)),tptp0),
inference(resolution,[status(thm)],[p525,c9]) ).
cnf(p3066,plain,
( subactivity_occurrence(sk10(sk13(sk15),sk14(sk15),tptp0),sk2(tptp0,sk13(sk15),sk14(sk15)))
| ~ subactivity_occurrence(sk14(sk15),sk2(tptp0,sk13(sk15),sk14(sk15))) ),
inference(resolution,[status(thm)],[p1079,p537]) ).
cnf(c11,plain,
( subactivity_occurrence(X2,sk2(X0,X1,X2))
| ~ min_precedes(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p539,plain,
subactivity_occurrence(sk14(sk15),sk2(tptp0,sk13(sk15),sk14(sk15))),
inference(resolution,[status(thm)],[p525,c11]) ).
cnf(p43379,plain,
subactivity_occurrence(sk10(sk13(sk15),sk14(sk15),tptp0),sk2(tptp0,sk13(sk15),sk14(sk15))),
inference(resolution,[status(thm)],[p3066,p539]) ).
fof(f19,axiom,
! [X58,X59] :
( root_occ(X58,X59)
<=> ? [X60] :
( root(X58,X60)
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,X60) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_19) ).
fof(f19_nnf,plain,
! [X58,X59] :
( ( ! [X60] :
( ~ root(X58,X60)
| ~ subactivity_occurrence(X58,X59)
| ~ occurrence_of(X59,X60) )
| root_occ(X58,X59) )
& ( ? [X60] :
( root(X58,X60)
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,X60) )
| ~ root_occ(X58,X59) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X58,X59,X60] :
( ( ~ root(X58,X60)
| ~ subactivity_occurrence(X58,X59)
| ~ occurrence_of(X59,X60)
| root_occ(X58,X59) )
& ( ( root(X58,sk9(X58,X59))
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,sk9(X58,X59)) )
| ~ root_occ(X58,X59) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f19_nnf]) ).
cnf(c40,plain,
( ~ root(X0,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,X2)
| root_occ(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p642,plain,
( ~ root(X0,tptp0)
| ~ subactivity_occurrence(X0,sk2(tptp0,sk13(sk15),sk14(sk15)))
| root_occ(X0,sk2(tptp0,sk13(sk15),sk14(sk15))) ),
inference(resolution,[status(thm)],[p537,c40]) ).
cnf(p43382,plain,
( ~ root(sk10(sk13(sk15),sk14(sk15),tptp0),tptp0)
| root_occ(sk10(sk13(sk15),sk14(sk15),tptp0),sk2(tptp0,sk13(sk15),sk14(sk15))) ),
inference(resolution,[status(thm)],[p43379,p642]) ).
cnf(c46,plain,
( root(sk10(X0,X1,X2),X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p542,plain,
root(sk10(sk13(sk15),sk14(sk15),tptp0),tptp0),
inference(resolution,[status(thm)],[p525,c46]) ).
cnf(p43385,plain,
root_occ(sk10(sk13(sk15),sk14(sk15),tptp0),sk2(tptp0,sk13(sk15),sk14(sk15))),
inference(resolution,[status(thm)],[p43382,p542]) ).
cnf(c63,plain,
( min_precedes(sk12(X0),sk13(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p464,plain,
min_precedes(sk12(sk15),sk13(sk15),tptp0),
inference(resolution,[status(thm)],[c63,c79]) ).
cnf(p523,plain,
( subactivity_occurrence(sk12(sk15),X0)
| ~ subactivity_occurrence(sk13(sk15),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[p464,c55]) ).
cnf(p1347,plain,
( subactivity_occurrence(sk12(sk15),sk2(tptp0,sk13(sk15),sk14(sk15)))
| ~ subactivity_occurrence(sk13(sk15),sk2(tptp0,sk13(sk15),sk14(sk15))) ),
inference(resolution,[status(thm)],[p523,p537]) ).
cnf(c10,plain,
( subactivity_occurrence(X1,sk2(X0,X1,X2))
| ~ min_precedes(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p538,plain,
subactivity_occurrence(sk13(sk15),sk2(tptp0,sk13(sk15),sk14(sk15))),
inference(resolution,[status(thm)],[p525,c10]) ).
cnf(p5509,plain,
subactivity_occurrence(sk12(sk15),sk2(tptp0,sk13(sk15),sk14(sk15))),
inference(resolution,[status(thm)],[p1347,p538]) ).
cnf(p5513,plain,
( ~ root(sk12(sk15),tptp0)
| root_occ(sk12(sk15),sk2(tptp0,sk13(sk15),sk14(sk15))) ),
inference(resolution,[status(thm)],[p5509,p642]) ).
cnf(c61,plain,
( root_occ(sk12(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p430,plain,
root_occ(sk12(sk15),sk15),
inference(resolution,[status(thm)],[c61,c79]) ).
cnf(c37,plain,
( occurrence_of(X1,sk9(X0,X1))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p435,plain,
occurrence_of(sk15,sk9(sk12(sk15),sk15)),
inference(resolution,[status(thm)],[p430,c37]) ).
fof(f8,axiom,
! [X28,X29,X30] :
( ( occurrence_of(X28,X30)
& occurrence_of(X28,X29) )
=> X29 = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(f8_nnf,plain,
! [X28,X29,X30] :
( X29 = X30
| ~ occurrence_of(X28,X30)
| ~ occurrence_of(X28,X29) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X28,X29,X30] :
( X29 = X30
| ~ occurrence_of(X28,X30)
| ~ occurrence_of(X28,X29) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c14,plain,
( X1 = X2
| ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p135,plain,
( tptp0 = X0
| ~ occurrence_of(sk15,X0) ),
inference(resolution,[status(thm)],[c14,c79]) ).
cnf(p486,plain,
tptp0 = sk9(sk12(sk15),sk15),
inference(resolution,[status(thm)],[p435,p135]) ).
cnf(c39,plain,
( root(X0,sk9(X0,X1))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p437,plain,
root(sk12(sk15),sk9(sk12(sk15),sk15)),
inference(resolution,[status(thm)],[p430,c39]) ).
cnf(p568,plain,
root(sk12(sk15),tptp0),
inference(superposition,[status(thm)],[p486,p437]) ).
cnf(p5514,plain,
root_occ(sk12(sk15),sk2(tptp0,sk13(sk15),sk14(sk15))),
inference(resolution,[status(thm)],[p5513,p568]) ).
fof(f29,axiom,
! [X90,X91,X92,X93] :
( ( root_occ(X91,X92)
& root_occ(X90,X92)
& occurrence_of(X92,X93) )
=> X90 = X91 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_29) ).
fof(f29_nnf,plain,
! [X90,X91,X92,X93] :
( X90 = X91
| ~ root_occ(X91,X92)
| ~ root_occ(X90,X92)
| ~ occurrence_of(X92,X93) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X92,X93,X90,X91] :
( X90 = X91
| ~ root_occ(X91,X92)
| ~ root_occ(X90,X92)
| ~ occurrence_of(X92,X93) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c57,plain,
( X0 = X1
| ~ root_occ(X1,X2)
| ~ root_occ(X0,X2)
| ~ occurrence_of(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p644,plain,
( X0 = X1
| ~ root_occ(X1,sk2(tptp0,sk13(sk15),sk14(sk15)))
| ~ root_occ(X0,sk2(tptp0,sk13(sk15),sk14(sk15))) ),
inference(resolution,[status(thm)],[p537,c57]) ).
cnf(p5518,plain,
( sk12(sk15) = X0
| ~ root_occ(X0,sk2(tptp0,sk13(sk15),sk14(sk15))) ),
inference(resolution,[status(thm)],[p5514,p644]) ).
cnf(p43391,plain,
sk12(sk15) = sk10(sk13(sk15),sk14(sk15),tptp0),
inference(resolution,[status(thm)],[p43385,p5518]) ).
cnf(p43394,plain,
min_precedes(sk12(sk15),sk14(sk15),tptp0),
inference(superposition,[status(thm)],[p43391,p543]) ).
cnf(c60,plain,
( occurrence_of(sk12(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p411,plain,
occurrence_of(sk12(sk15),tptp3),
inference(resolution,[status(thm)],[c60,c79]) ).
cnf(c81,plain,
( ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp1)
| ~ root_occ(X1,sk15)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p415,plain,
( ~ min_precedes(sk12(sk15),X0,tptp0)
| ~ occurrence_of(X0,tptp1)
| ~ root_occ(sk12(sk15),sk15) ),
inference(resolution,[status(thm)],[p411,c81]) ).
cnf(p1657,plain,
( ~ min_precedes(sk12(sk15),X0,tptp0)
| ~ occurrence_of(X0,tptp1) ),
inference(resolution,[status(thm)],[p415,p430]) ).
cnf(c64,plain,
( occurrence_of(sk14(X0),tptp1)
| occurrence_of(sk14(X0),tptp2)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p495,plain,
( occurrence_of(sk14(sk15),tptp1)
| occurrence_of(sk14(sk15),tptp2) ),
inference(resolution,[status(thm)],[c64,c79]) ).
cnf(p1658,plain,
( occurrence_of(sk14(sk15),tptp2)
| ~ min_precedes(sk12(sk15),sk14(sk15),tptp0) ),
inference(resolution,[status(thm)],[p1657,p495]) ).
cnf(p43616,plain,
occurrence_of(sk14(sk15),tptp2),
inference(resolution,[status(thm)],[p43394,p1658]) ).
cnf(c80,plain,
( ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp2)
| ~ root_occ(X1,sk15)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p414,plain,
( ~ min_precedes(sk12(sk15),X0,tptp0)
| ~ occurrence_of(X0,tptp2)
| ~ root_occ(sk12(sk15),sk15) ),
inference(resolution,[status(thm)],[p411,c80]) ).
cnf(p1637,plain,
( ~ min_precedes(sk12(sk15),X0,tptp0)
| ~ occurrence_of(X0,tptp2) ),
inference(resolution,[status(thm)],[p414,p430]) ).
cnf(p46128,plain,
~ min_precedes(sk12(sk15),sk14(sk15),tptp0),
inference(resolution,[status(thm)],[p43616,p1637]) ).
cnf(p46132,plain,
$false,
inference(resolution,[status(thm)],[p46128,p43394]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PRO012+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Thu Sep 24 06:33:40 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 276.69/35.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 276.69/35.68 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------