%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW348+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:30:10 PM UTC 2026
% Result : Theorem 4.23s 1.72s
% Output : Refutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 69 ( 40 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 27 |; 4 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 49 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X0))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com__det) ).
fof(f4,axiom,
( c_Hoare__Mirabelle_Ostate__not__singleton
=> ! [X0] :
~ ! [X1] : X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__stateE) ).
fof(f5226,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5227,conjecture,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X0),X3))
=> X2 = X3 )
=> X2 = X1 )
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5228,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X0),X3))
=> X2 = X3 )
=> X2 = X1 )
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X0),X1)) ),
inference(negated_conjecture,[status(cth)],[f5227]) ).
fof(f5229,plain,
? [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X0),X1))
& ! [X2] :
( X2 = X1
| ? [X3] :
( X2 != X3
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X0),X3)) ) ) ),
inference(ennf_transformation,[],[f5228]) ).
fof(f5230,plain,
( ! [X0] :
? [X1] : X0 != X1
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(ennf_transformation,[],[f4]) ).
fof(f5240,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X1)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f5241,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X1)) ),
inference(flattening,[],[f5240]) ).
fof(f5242,plain,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),sK0),sK1))
& ! [X2] :
( sK1 = X2
| ( sK2(X2) != X2
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),sK0),sK2(X2))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2))],[f5229]) ).
fof(f5243,plain,
( ! [X0] : sK3(X0) != X0
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f5230]) ).
fof(f5261,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnf_transformation,[],[f5226]) ).
fof(f5262,plain,
! [X2] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),sK0),sK2(X2)))
| sK1 = X2 ),
inference(cnf_transformation,[],[f5242]) ).
fof(f5263,plain,
! [X2] :
( sK2(X2) != X2
| sK1 = X2 ),
inference(cnf_transformation,[],[f5242]) ).
fof(f5264,plain,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),sK0),sK1)),
inference(cnf_transformation,[],[f5242]) ).
fof(f5265,plain,
! [X0] :
( sK3(X0) != X0
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(cnf_transformation,[],[f5243]) ).
fof(f5293,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X0))
| X0 = X1 ),
inference(cnf_transformation,[],[f5241]) ).
fof(f5311,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),sK0),X1))
| sK1 = X0
| sK2(X0) = X1 ),
inference(resolution,[],[f5262,f5293]) ).
fof(f5324,plain,
! [X0,X1] :
( sK2(X0) = sK2(X1)
| sK1 = X0
| sK1 = X1 ),
inference(resolution,[],[f5311,f5262]) ).
fof(f5351,plain,
! [X0,X1] :
( sK2(X0) != X1
| sK1 = X1
| sK1 = X0
| sK1 = X1 ),
inference(superposition,[],[f5263,f5324]) ).
fof(f5352,plain,
! [X0,X1] :
( sK2(X0) != X1
| sK1 = X1
| sK1 = X0 ),
inference(duplicate_literal_removal,[],[f5351]) ).
fof(f5364,plain,
! [X0] :
( sK1 = sK2(X0)
| sK1 = X0 ),
inference(equality_resolution,[],[f5352]) ).
fof(f5398,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),sK0),sK1))
| sK1 = X0
| sK1 = X0 ),
inference(superposition,[],[f5262,f5364]) ).
fof(f5402,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),sK0),sK1))
| sK1 = X0 ),
inference(duplicate_literal_removal,[],[f5398]) ).
fof(f5408,plain,
! [X0] : sK1 = X0,
inference(forward_subsumption_resolution,[],[f5402,f5264]) ).
fof(f5425,plain,
! [X0,X1] : X0 = X1,
inference(superposition,[],[f5408,f5408]) ).
fof(f5551,plain,
! [X0] :
( sK1 != X0
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(superposition,[],[f5265,f5408]) ).
fof(f5578,plain,
! [X0] : sK1 != X0,
inference(forward_subsumption_resolution,[],[f5551,f5261]) ).
fof(f5715,plain,
$false,
inference(forward_subsumption_resolution,[],[f5578,f5425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW348+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n017.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 13:35:22 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.23/1.72 % (3552382)Detected formulas, will run a generic FOF schedule.
% 4.23/1.72 % (3552392)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3841872999:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 4.23/1.72 % (3552392)Instruction limit reached!
% 4.23/1.72 % (3552392)------------------------------
% 4.23/1.72 % (3552392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.72 % (3552392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.72 % (3552392)CaDiCaL version: 2.1.3
% 4.23/1.72 % (3552392)Termination reason: Instruction limit
% 4.23/1.72 % (3552392)Termination phase: SInE selection
% 4.23/1.72 % (3552392)Time elapsed: 0.032 s
% 4.23/1.72 % (3552392)Peak memory usage: 90 MB
% 4.23/1.72 % (3552392)Instructions burned: 139 (million)
% 4.23/1.72 % (3552391)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3837799094:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 4.23/1.72 % (3552388)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=761349815:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 4.23/1.72 % (3552393)dis-21_1_sil=8000:lcm=predicate:random_seed=4273776766:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2995 on theBenchmark for (2995ds/129Mi)
% 4.23/1.72 % (3552387)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=1714304146:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 4.23/1.72 % (3552389)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=1451500172:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 4.23/1.72 % (3552390)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2100448259:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 4.23/1.72 % (3552390)First to succeed.
% 4.23/1.72 % (3552390)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3552382"
% 4.23/1.72 % (3552391)Instruction limit reached!
% 4.23/1.72 % (3552391)------------------------------
% 4.23/1.72 % (3552391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.72 % (3552391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.72 % (3552391)CaDiCaL version: 2.1.3
% 4.23/1.72 % (3552391)Termination reason: Instruction limit
% 4.23/1.72 % (3552391)Termination phase: Saturation
% 4.23/1.72 % (3552391)Time elapsed: 0.075 s
% 4.23/1.72 % (3552391)Peak memory usage: 94 MB
% 4.23/1.72 % (3552391)Instructions burned: 119 (million)
% 4.23/1.72 % (3552395)lrs+10_1_sil=8000:sp=occurrence:random_seed=305807288:i=285:sd=3:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/285Mi)
% 4.23/1.72 % (3552393)Instruction limit reached!
% 4.23/1.72 % (3552393)------------------------------
% 4.23/1.72 % (3552393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.72 % (3552393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.72 % (3552393)CaDiCaL version: 2.1.3
% 4.23/1.72 % (3552393)Termination reason: Instruction limit
% 4.23/1.72 % (3552393)Termination phase: Preprocessing 3
% 4.23/1.72 % (3552393)Time elapsed: 0.085 s
% 4.23/1.72 % (3552393)Peak memory usage: 93 MB
% 4.23/1.72 % (3552393)Instructions burned: 129 (million)
% 4.23/1.72 % (3552395)Also succeeded, but the first one will report.
% 4.23/1.72 % (3552403)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3483142777:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 4.23/1.72 % (3552404)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3153082888:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 4.23/1.72 % (3552404)Also succeeded, but the first one will report.
% 4.23/1.72 % (3552403)Instruction limit reached!
% 4.23/1.72 % (3552403)------------------------------
% 4.23/1.72 % (3552403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.72 % (3552390)Refutation found. Thanks to Tanya!
% 4.23/1.72 % SZS status Theorem for theBenchmark
% 4.23/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 4.23/1.72 % (3552390)------------------------------
% 4.23/1.72 % (3552390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.72 % (3552390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.72 % (3552390)CaDiCaL version: 2.1.3
% 4.23/1.72 % (3552390)Termination reason: Refutation
% 4.23/1.72 % (3552390)Time elapsed: 0.035 s
% 4.23/1.72 % (3552390)Peak memory usage: 94 MB
% 4.23/1.72 % (3552390)Instructions burned: 46 (million)
% 4.23/1.72 % (3552390)------------------------------
% 4.23/1.72 % (3552390)------------------------------
% 4.23/1.72 % (3552382)Success in time 0.85 s
% 4.23/1.72 % Vampire exiting
%------------------------------------------------------------------------------