%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT161+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Tue Sep 29 12:37:03 PM UTC 2026
% Result : ContradictoryAxioms 3.89s 1.47s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 22 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 65 ( 59 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f60,axiom,
! [X0,X1,X2,X3] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(f149,axiom,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X3,X2)
=> c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(f156,axiom,
! [X0,X1,X2] :
( c_Finite__Set_Ofinite(X2,X1)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0),X1))
=> c_Finite__Set_Ofinite(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(f211,axiom,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(f227,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(f253,axiom,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(f283,axiom,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f600,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) ),
inference(ennf_transformation,[],[f253]) ).
fof(f602,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0),X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(ennf_transformation,[],[f156]) ).
fof(f603,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0),X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(flattening,[],[f602]) ).
fof(f627,plain,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(ennf_transformation,[],[f149]) ).
fof(f865,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f600]) ).
fof(f866,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f865]) ).
fof(f867,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK5(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK5(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),sK6(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0))],[f866]) ).
fof(f991,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(cnf_transformation,[],[f227]) ).
fof(f1002,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f211]) ).
fof(f1009,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
inference(cnf_transformation,[],[f60]) ).
fof(f1091,plain,
! [X0,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),sK6(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f867]) ).
fof(f1097,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X0),X1))
| c_Finite__Set_Ofinite(X2,X0)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(cnf_transformation,[],[f603]) ).
fof(f1119,plain,
! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(cnf_transformation,[],[f627]) ).
fof(f1339,plain,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),X0)),
inference(cnf_transformation,[],[f283]) ).
fof(f1700,plain,
! [X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X0,X1) ),
inference(resolution,[],[f1097,f1002]) ).
fof(f1703,plain,
! [X0] : c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X0),
inference(resolution,[],[f1700,f991]) ).
fof(f2942,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_OSuc,sK6(X0))),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(resolution,[],[f1091,f1339]) ).
fof(f2952,plain,
! [X0] : ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X0,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
inference(resolution,[],[f2942,f1009]) ).
fof(f3250,plain,
! [X0] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(resolution,[],[f2952,f1119]) ).
fof(f3272,plain,
$false,
inference(resolution,[],[f3250,f1703]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT161+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n008.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 23:52:25 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.89/1.47 % (1733582)Detected formulas, will run a generic FOF schedule.
% 3.89/1.47 % (1733587)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3465492671:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.89/1.47 % (1733592)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1727937563:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.89/1.47 % (1733593)dis-21_1_sil=8000:lcm=predicate:random_seed=2135091933:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.89/1.47 % (1733589)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2623435111:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.89/1.47 % (1733588)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=850452776:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.89/1.47 % (1733590)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1578082361:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.89/1.47 % (1733591)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=509396340:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.89/1.47 % (1733590)Instruction limit reached!
% 3.89/1.47 % (1733590)------------------------------
% 3.89/1.47 % (1733590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.47 % (1733591)First to succeed.
% 3.89/1.47 % (1733590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.47 % (1733590)CaDiCaL version: 2.1.3
% 3.89/1.47 % (1733590)Termination reason: Instruction limit
% 3.89/1.47 % (1733590)Termination phase: Saturation
% 3.89/1.47 % (1733590)Time elapsed: 0.069 s
% 3.89/1.47 % (1733590)Peak memory usage: 89 MB
% 3.89/1.47 % (1733590)Instructions burned: 110 (million)
% 3.89/1.47 % (1733591)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1733582"
% 3.89/1.47 % (1733593)Instruction limit reached!
% 3.89/1.47 % (1733593)------------------------------
% 3.89/1.47 % (1733593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.47 % (1733593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.47 % (1733593)CaDiCaL version: 2.1.3
% 3.89/1.47 % (1733593)Termination reason: Instruction limit
% 3.89/1.47 % (1733593)Termination phase: Saturation
% 3.89/1.47 % (1733593)Time elapsed: 0.070 s
% 3.89/1.47 % (1733593)Peak memory usage: 90 MB
% 3.89/1.47 % (1733593)Instructions burned: 130 (million)
% 3.89/1.47 % (1733592)Instruction limit reached!
% 3.89/1.47 % (1733592)------------------------------
% 3.89/1.47 % (1733592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.47 % (1733592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.47 % (1733592)CaDiCaL version: 2.1.3
% 3.89/1.47 % (1733592)Termination reason: Instruction limit
% 3.89/1.47 % (1733592)Termination phase: Saturation
% 3.89/1.47 % (1733592)Time elapsed: 0.081 s
% 3.89/1.47 % (1733592)Peak memory usage: 90 MB
% 3.89/1.47 % (1733592)Instructions burned: 140 (million)
% 3.89/1.47 % (1733602)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1480965966:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.89/1.47 % (1733601)lrs+10_1_sil=8000:sp=occurrence:random_seed=2859368699:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.89/1.47 % (1733603)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1911588361:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.89/1.47 % (1733602)Instruction limit reached!
% 3.89/1.47 % (1733602)------------------------------
% 3.89/1.47 % (1733602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.47 % (1733602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.47 % (1733602)CaDiCaL version: 2.1.3
% 3.89/1.47 % (1733602)Termination reason: Instruction limit
% 3.89/1.47 % (1733602)Termination phase: Saturation
% 3.89/1.47 % (1733602)Time elapsed: 0.085 s
% 3.89/1.47 % (1733602)Peak memory usage: 90 MB
% 3.89/1.47 % (1733602)Instructions burned: 157 (million)
% 3.89/1.47 % (1733591)Refutation found. Thanks to Tanya!
% 3.89/1.47 % SZS status ContradictoryAxioms for theBenchmark
% 3.89/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.47 % (1733591)------------------------------
% 3.89/1.47 % (1733591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.47 % (1733591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.47 % (1733591)CaDiCaL version: 2.1.3
% 3.89/1.47 % (1733591)Termination reason: Refutation
% 3.89/1.47 % (1733591)Time elapsed: 0.070 s
% 3.89/1.47 % (1733591)Peak memory usage: 90 MB
% 3.89/1.47 % (1733591)Instructions burned: 118 (million)
% 3.89/1.47 % (1733591)------------------------------
% 3.89/1.47 % (1733591)------------------------------
% 3.89/1.47 % (1733582)Success in time 0.508 s
% 3.89/1.47 % Vampire exiting
%------------------------------------------------------------------------------