%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW349+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 : n003.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 4.15s 1.71s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 65 ( 38 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 25 ~; 27 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 45 ( 43 !; 2 ?)
% 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,axiom,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),X1))
=> X0 = X1 )
=> X0 = v_s_H ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5228,conjecture,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f5229,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
inference(negated_conjecture,[status(cth)],[f5228]) ).
fof(f5230,plain,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
inference(flattening,[],[f5229]) ).
fof(f5231,plain,
! [X0] :
( X0 = v_s_H
| ? [X1] :
( X0 != X1
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),X1)) ) ),
inference(ennf_transformation,[],[f5227]) ).
fof(f5232,plain,
( ! [X0] :
? [X1] : X0 != X1
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(ennf_transformation,[],[f4]) ).
fof(f5236,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(f5237,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,[],[f5236]) ).
fof(f5238,plain,
! [X0] :
( X0 = v_s_H
| ( sK0(X0) != X0
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),sK0(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f5231]) ).
fof(f5239,plain,
( ! [X0] : sK1(X0) != X0
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f5232]) ).
fof(f5248,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnf_transformation,[],[f5226]) ).
fof(f5249,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),sK0(X0)))
| v_s_H = X0 ),
inference(cnf_transformation,[],[f5238]) ).
fof(f5250,plain,
! [X0] :
( sK0(X0) != X0
| v_s_H = X0 ),
inference(cnf_transformation,[],[f5238]) ).
fof(f5251,plain,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
inference(cnf_transformation,[],[f5230]) ).
fof(f5252,plain,
! [X0] :
( sK1(X0) != X0
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(cnf_transformation,[],[f5239]) ).
fof(f5260,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,[],[f5237]) ).
fof(f5277,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),X1))
| v_s_H = X0
| sK0(X0) = X1 ),
inference(resolution,[],[f5249,f5260]) ).
fof(f5290,plain,
! [X0,X1] :
( sK0(X0) = sK0(X1)
| v_s_H = X0
| v_s_H = X1 ),
inference(resolution,[],[f5277,f5249]) ).
fof(f5312,plain,
! [X0,X1] :
( sK0(X0) != X1
| v_s_H = X1
| v_s_H = X0
| v_s_H = X1 ),
inference(superposition,[],[f5250,f5290]) ).
fof(f5313,plain,
! [X0,X1] :
( sK0(X0) != X1
| v_s_H = X1
| v_s_H = X0 ),
inference(duplicate_literal_removal,[],[f5312]) ).
fof(f5325,plain,
! [X0] :
( v_s_H = sK0(X0)
| v_s_H = X0 ),
inference(equality_resolution,[],[f5313]) ).
fof(f5339,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H))
| v_s_H = X0
| v_s_H = X0 ),
inference(superposition,[],[f5249,f5325]) ).
fof(f5343,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H))
| v_s_H = X0 ),
inference(duplicate_literal_removal,[],[f5339]) ).
fof(f5349,plain,
! [X0] : v_s_H = X0,
inference(forward_subsumption_resolution,[],[f5343,f5251]) ).
fof(f5351,plain,
! [X0,X1] : X0 = X1,
inference(superposition,[],[f5349,f5349]) ).
fof(f5398,plain,
! [X0] :
( v_s_H != X0
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(superposition,[],[f5252,f5349]) ).
fof(f5405,plain,
! [X0] : v_s_H != X0,
inference(forward_subsumption_resolution,[],[f5398,f5248]) ).
fof(f5431,plain,
$false,
inference(forward_subsumption_resolution,[],[f5405,f5351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW349+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 13:41:43 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.15/1.71 % (1583964)Detected formulas, will run a generic FOF schedule.
% 4.15/1.71 % (1583971)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=1964693852:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 4.15/1.71 % (1583975)dis-21_1_sil=8000:lcm=predicate:random_seed=3920381592: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)
% 4.15/1.71 % (1583974)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3533865330:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 4.15/1.71 % (1583969)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=3968369147:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 4.15/1.71 % (1583972)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3723333745:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 4.15/1.71 % (1583973)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1037671498:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 4.15/1.71 % (1583970)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=1863539729:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 4.15/1.71 % (1583972)First to succeed.
% 4.15/1.71 % (1583972)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1583964"
% 4.15/1.71 % (1583974)Instruction limit reached!
% 4.15/1.71 % (1583974)------------------------------
% 4.15/1.71 % (1583974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.71 % (1583974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.71 % (1583974)CaDiCaL version: 2.1.3
% 4.15/1.71 % (1583974)Termination reason: Instruction limit
% 4.15/1.71 % (1583974)Termination phase: SInE selection
% 4.15/1.71 % (1583974)Time elapsed: 0.057 s
% 4.15/1.71 % (1583974)Peak memory usage: 90 MB
% 4.15/1.71 % (1583974)Instructions burned: 140 (million)
% 4.15/1.71 % (1583973)Also succeeded, but the first one will report.
% 4.15/1.71 % (1583975)Instruction limit reached!
% 4.15/1.71 % (1583975)------------------------------
% 4.15/1.71 % (1583975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.71 % (1583975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.71 % (1583975)CaDiCaL version: 2.1.3
% 4.15/1.71 % (1583975)Termination reason: Instruction limit
% 4.15/1.71 % (1583975)Termination phase: Preprocessing 3
% 4.15/1.71 % (1583975)Time elapsed: 0.106 s
% 4.15/1.71 % (1583975)Peak memory usage: 93 MB
% 4.15/1.71 % (1583975)Instructions burned: 129 (million)
% 4.15/1.71 % (1583983)lrs+10_1_sil=8000:sp=occurrence:random_seed=2769981721:i=285:sd=3:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/285Mi)
% 4.15/1.71 % (1583984)lrs+10_1_sil=32000:urr=on:br=off:random_seed=844339491:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 4.15/1.71 % (1583972)Refutation found. Thanks to Tanya!
% 4.15/1.71 % SZS status Theorem for theBenchmark
% 4.15/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 4.15/1.71 % (1583972)------------------------------
% 4.15/1.71 % (1583972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.71 % (1583972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.71 % (1583972)CaDiCaL version: 2.1.3
% 4.15/1.71 % (1583972)Termination reason: Refutation
% 4.15/1.71 % (1583972)Time elapsed: 0.028 s
% 4.15/1.71 % (1583972)Peak memory usage: 94 MB
% 4.15/1.71 % (1583972)Instructions burned: 37 (million)
% 4.15/1.71 % (1583972)------------------------------
% 4.15/1.71 % (1583972)------------------------------
% 4.15/1.71 % (1583964)Success in time 0.839 s
% 4.15/1.71 % Vampire exiting
%------------------------------------------------------------------------------