%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT159+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 4.18s 1.48s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 66 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 29 ~; 24 |; 6 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 76 ( 70 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,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(f13,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(f110,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
=> ( c_Finite__Set_Ofinite(X2,X0)
=> c_Finite__Set_Ofinite(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(f173,axiom,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( c_member(tc_Nat_Onat,X2,X0)
=> 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(f195,axiom,
! [X0,X1] : 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(f209,axiom,
! [X0,X1,X2,X3,X4] :
( X4 = hAPP(X3,X2)
=> c_member(X1,X4,c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(f243,axiom,
! [X0] : ~ 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(f566,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,[],[f13]) ).
fof(f613,plain,
! [X0,X1,X2,X3,X4] :
( c_member(X1,X4,c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))
| hAPP(X3,X2) != X4 ),
inference(ennf_transformation,[],[f209]) ).
fof(f681,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_member(tc_Nat_Onat,X2,X0) ) ),
inference(ennf_transformation,[],[f173]) ).
fof(f685,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f110]) ).
fof(f686,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(flattening,[],[f685]) ).
fof(f914,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
& c_member(tc_Nat_Onat,X2,X0) ) )
& ( ? [X1] :
! [X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_member(tc_Nat_Onat,X2,X0) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f681]) ).
fof(f915,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
& c_member(tc_Nat_Onat,X2,X0) ) )
& ( ? [X3] :
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| ~ c_member(tc_Nat_Onat,X4,X0) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f914]) ).
fof(f916,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK20(X0,X1),X1)
& c_member(tc_Nat_Onat,sK20(X0,X1),X0) ) )
& ( ! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,sK21(X0))
| ~ c_member(tc_Nat_Onat,X4,X0) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X2,sK20(X0,X1)),skolemize(X3,sK21(X0))],[f915]) ).
fof(f998,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,[],[f566]) ).
fof(f1059,plain,
! [X2,X3,X0,X1,X4] :
( c_member(X1,X4,c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))
| hAPP(X3,X2) != X4 ),
inference(cnf_transformation,[],[f613]) ).
fof(f1060,plain,
! [X0,X1] : 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,[],[f195]) ).
fof(f1099,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,[],[f12]) ).
fof(f1197,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0),X0),
inference(cnf_transformation,[],[f243]) ).
fof(f1244,plain,
! [X0,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,sK21(X0))
| ~ c_member(tc_Nat_Onat,X4,X0)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f916]) ).
fof(f1251,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Finite__Set_Ofinite(X2,X0)
| c_Finite__Set_Ofinite(X2,X1) ),
inference(cnf_transformation,[],[f686]) ).
fof(f1439,plain,
! [X2,X3,X0,X1] : c_member(X1,hAPP(X3,X2),c_Set_Oimage(X0,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
inference(equality_resolution,[],[f1059]) ).
fof(f2689,plain,
! [X0] :
( ~ c_member(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK21(X0)),X0)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(resolution,[],[f1244,f1197]) ).
fof(f2758,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,[],[f1251,f1060]) ).
fof(f2776,plain,
! [X0] : c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X0),
inference(resolution,[],[f2758,f1099]) ).
fof(f3598,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,[],[f2689,f1439]) ).
fof(f4306,plain,
! [X0] : ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(resolution,[],[f3598,f998]) ).
fof(f4383,plain,
$false,
inference(resolution,[],[f4306,f2776]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT159+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 23:52:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 4.18/1.48 % (1733175)Detected formulas, will run a generic FOF schedule.
% 4.18/1.48 % (1733185)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=613455441:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.18/1.48 % (1733182)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=3769515783:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.18/1.48 % (1733183)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2933099487:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.18/1.48 % (1733181)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=3278546322:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.18/1.48 % (1733180)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=2248380322:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.18/1.48 % (1733184)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4288760688:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.18/1.48 % (1733186)dis-21_1_sil=8000:lcm=predicate:random_seed=3048853415: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)
% 4.18/1.48 % (1733185)Instruction limit reached!
% 4.18/1.48 % (1733185)------------------------------
% 4.18/1.48 % (1733185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.48 % (1733185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.48 % (1733185)CaDiCaL version: 2.1.3
% 4.18/1.48 % (1733185)Termination reason: Instruction limit
% 4.18/1.48 % (1733185)Termination phase: Saturation
% 4.18/1.48 % (1733185)Time elapsed: 0.052 s
% 4.18/1.48 % (1733185)Peak memory usage: 90 MB
% 4.18/1.48 % (1733185)Instructions burned: 140 (million)
% 4.18/1.48 % (1733183)Instruction limit reached!
% 4.18/1.48 % (1733183)------------------------------
% 4.18/1.48 % (1733183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.48 % (1733183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.48 % (1733183)CaDiCaL version: 2.1.3
% 4.18/1.48 % (1733183)Termination reason: Instruction limit
% 4.18/1.48 % (1733183)Termination phase: Saturation
% 4.18/1.48 % (1733183)Time elapsed: 0.073 s
% 4.18/1.48 % (1733183)Peak memory usage: 89 MB
% 4.18/1.48 % (1733183)Instructions burned: 109 (million)
% 4.18/1.48 % (1733184)Instruction limit reached!
% 4.18/1.48 % (1733184)------------------------------
% 4.18/1.48 % (1733184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.48 % (1733184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.48 % (1733184)CaDiCaL version: 2.1.3
% 4.18/1.48 % (1733184)Termination reason: Instruction limit
% 4.18/1.48 % (1733184)Termination phase: Saturation
% 4.18/1.48 % (1733184)Time elapsed: 0.074 s
% 4.18/1.48 % (1733184)Peak memory usage: 89 MB
% 4.18/1.48 % (1733184)Instructions burned: 120 (million)
% 4.18/1.48 % (1733186)Instruction limit reached!
% 4.18/1.48 % (1733186)------------------------------
% 4.18/1.48 % (1733186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.48 % (1733186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.48 % (1733186)CaDiCaL version: 2.1.3
% 4.18/1.48 % (1733186)Termination reason: Instruction limit
% 4.18/1.48 % (1733186)Termination phase: Saturation
% 4.18/1.48 % (1733186)Time elapsed: 0.073 s
% 4.18/1.48 % (1733186)Peak memory usage: 90 MB
% 4.18/1.48 % (1733186)Instructions burned: 131 (million)
% 4.18/1.48 % (1733194)lrs+10_1_sil=8000:sp=occurrence:random_seed=2938787395:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.18/1.48 % (1733194)First to succeed.
% 4.18/1.48 % (1733194)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1733175"
% 4.18/1.48 % (1733196)lrs+1011_1_sil=32000:sp=occurrence:random_seed=540997313:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.18/1.48 % (1733195)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3334466845:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.18/1.48 % (1733195)Refutation not found, incomplete strategy
% 4.18/1.48 % (1733195)------------------------------
% 4.18/1.48 % (1733195)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.48 % (1733195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.48 % (1733195)CaDiCaL version: 2.1.3
% 4.18/1.48 % (1733195)Termination reason: Refutation not found, incomplete strategy
% 4.18/1.48 % (1733195)Time elapsed: 0.004 s
% 4.18/1.48 % (1733195)Peak memory usage: 87 MB
% 4.18/1.48 % (1733195)Instructions burned: 6 (million)
% 4.18/1.48 % (1733197)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1860973481:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.18/1.48 % (1733194)Refutation found. Thanks to Tanya!
% 4.18/1.48 % SZS status ContradictoryAxioms for theBenchmark
% 4.18/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 4.18/1.48 % (1733194)------------------------------
% 4.18/1.48 % (1733194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.48 % (1733194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.48 % (1733194)CaDiCaL version: 2.1.3
% 4.18/1.48 % (1733194)Termination reason: Refutation
% 4.18/1.48 % (1733194)Time elapsed: 0.045 s
% 4.18/1.48 % (1733194)Peak memory usage: 90 MB
% 4.18/1.48 % (1733194)Instructions burned: 128 (million)
% 4.18/1.48 % (1733194)------------------------------
% 4.18/1.48 % (1733194)------------------------------
% 4.18/1.48 % (1733175)Success in time 0.543 s
% 4.18/1.48 % Vampire exiting
%------------------------------------------------------------------------------