%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW469+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 01:30:24 PM UTC 2026
% Result : Theorem 4.23s 1.37s
% Output : Refutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 12 unt; 1 def)
% Number of atoms : 32 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 9 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 18 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
( hBOOL(hoare_1883395792gleton)
<=> ? [X0,X1] : ti(state,X0) != ti(state,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
fof(f62,axiom,
hBOOL(hoare_1883395792gleton),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f63,conjecture,
! [X0] :
~ ! [X1] : ti(state,X1) = ti(state,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f64,negated_conjecture,
~ ! [X0] :
~ ! [X1] : ti(state,X1) = ti(state,X0),
inference(negated_conjecture,[status(cth)],[f63]) ).
fof(f65,plain,
? [X0] :
! [X1] : ti(state,X1) = ti(state,X0),
inference(ennf_transformation,[],[f64]) ).
fof(f67,plain,
! [X1] : ti(state,X1) = ti(state,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f65]) ).
fof(f68,plain,
( ( hBOOL(hoare_1883395792gleton)
| ! [X0,X1] : ti(state,X0) = ti(state,X1) )
& ( ? [X0,X1] : ti(state,X0) != ti(state,X1)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f69,plain,
( ( hBOOL(hoare_1883395792gleton)
| ! [X0,X1] : ti(state,X0) = ti(state,X1) )
& ( ? [X2,X3] : ti(state,X2) != ti(state,X3)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
( ( hBOOL(hoare_1883395792gleton)
| ! [X0,X1] : ti(state,X0) = ti(state,X1) )
& ( ti(state,sK1) != ti(state,sK2)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X2,sK1),skolemize(X3,sK2)],[f69]) ).
fof(f74,plain,
hBOOL(hoare_1883395792gleton),
inference(cnf_transformation,[],[f62]) ).
fof(f75,plain,
! [X1] : ti(state,X1) = ti(state,sK0),
inference(cnf_transformation,[],[f67]) ).
fof(f77,plain,
( ti(state,sK1) != ti(state,sK2)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(cnf_transformation,[],[f70]) ).
fof(f79,definition,
~ sP3(ti(state,sK1)),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f80,plain,
( sP3(ti(state,sK2))
| ~ hBOOL(hoare_1883395792gleton) ),
inference(inequality_splitting,[],[f77,f79]) ).
fof(f84,plain,
! [X0,X1] : ti(state,X0) = ti(state,X1),
inference(superposition,[],[f75,f75]) ).
fof(f120,plain,
! [X0] : ~ sP3(ti(state,X0)),
inference(superposition,[],[f79,f84]) ).
fof(f121,plain,
! [X0] :
( sP3(ti(state,X0))
| ~ hBOOL(hoare_1883395792gleton) ),
inference(superposition,[],[f80,f84]) ).
fof(f124,plain,
! [X0] : sP3(ti(state,X0)),
inference(forward_subsumption_resolution,[],[f121,f74]) ).
fof(f126,plain,
$false,
inference(forward_subsumption_resolution,[],[f124,f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW469+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n003.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 14:02:57 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 4.23/1.37 % (1593372)Detected formulas, will run a generic FOF schedule.
% 4.23/1.37 % (1593518)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=455087109:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.23/1.37 % (1593519)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1670051709:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.23/1.37 % (1593519)First to succeed.
% 4.23/1.37 % (1593519)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1593372"
% 4.23/1.37 % (1593516)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=1514504924:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.23/1.37 % (1593517)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=3202581103:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.23/1.37 % (1593526)dis-21_1_sil=8000:lcm=predicate:random_seed=3554787887: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)
% 4.23/1.37 % (1593521)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=808694189:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.23/1.37 % (1593521)Also succeeded, but the first one will report.
% 4.23/1.37 % (1593524)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1998624536:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.23/1.37 % (1593524)Also succeeded, but the first one will report.
% 4.23/1.37 % (1593526)Instruction limit reached!
% 4.23/1.37 % (1593526)------------------------------
% 4.23/1.37 % (1593526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.37 % (1593526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.37 % (1593526)CaDiCaL version: 2.1.3
% 4.23/1.37 % (1593526)Termination reason: Instruction limit
% 4.23/1.37 % (1593526)Termination phase: Saturation
% 4.23/1.37 % (1593526)Time elapsed: 0.103 s
% 4.23/1.37 % (1593526)Peak memory usage: 89 MB
% 4.23/1.37 % (1593526)Instructions burned: 130 (million)
% 4.23/1.37 % (1593584)lrs+10_1_sil=8000:sp=occurrence:random_seed=124831612:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 4.23/1.37 % (1593519)Refutation found. Thanks to Tanya!
% 4.23/1.37 % SZS status Theorem for theBenchmark
% 4.23/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 4.23/1.37 % (1593519)------------------------------
% 4.23/1.37 % (1593519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.37 % (1593519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.37 % (1593519)CaDiCaL version: 2.1.3
% 4.23/1.37 % (1593519)Termination reason: Refutation
% 4.23/1.37 % (1593519)Time elapsed: 0.004 s
% 4.23/1.37 % (1593519)Peak memory usage: 88 MB
% 4.23/1.37 % (1593519)Instructions burned: 2 (million)
% 4.23/1.37 % (1593519)------------------------------
% 4.23/1.37 % (1593519)------------------------------
% 4.23/1.37 % (1593372)Success in time 0.514 s
% 4.23/1.37 % Vampire exiting
%------------------------------------------------------------------------------