%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 01:39:33 PM UTC 2026
% Result : Theorem 0.37s 0.26s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 105 ( 39 unt; 4 def)
% Number of atoms : 218 ( 101 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 198 ( 85 ~; 77 |; 27 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( bool(X0)
<=> ( X0 = false
| X0 = true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_bool) ).
fof(f2,axiom,
( true != false
& true != err
& false != err ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',distinct_false_true_err) ).
fof(f3,axiom,
( d(true)
& d(false)
& d(err) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).
fof(f4,axiom,
! [X0,X1] :
( forallprefers(X0,X1)
<=> ( ( ~ d(X0)
& d(X1) )
| ( d(X0)
& d(X1)
& ~ bool(X0)
& bool(X1) )
| ( X0 = false
& X1 = true ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).
fof(f6,axiom,
! [X0] :
( ( d(X0)
& phi(X0) = X0 )
| ( ~ d(X0)
& phi(X0) = err ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_phi) ).
fof(f7,axiom,
! [X0] :
( prop(X0) = true
<=> bool(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_true) ).
fof(f8,axiom,
! [X0] :
( prop(X0) = false
<=> ~ bool(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_false) ).
fof(f14,axiom,
! [X0] : lazy_impl(false,X0) = true,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom2) ).
fof(f15,axiom,
! [X0] : lazy_impl(true,X0) = phi(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom3) ).
fof(f38,axiom,
false1 = false,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false1) ).
fof(f39,axiom,
! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f7) ).
fof(f40,axiom,
? [X0] :
( false2 = phi(f7(X0))
& ~ ? [X1] : forallprefers(f7(X1),f7(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false2) ).
fof(f45,conjecture,
false1 = false2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false1_false2) ).
fof(f46,negated_conjecture,
false1 != false2,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
false1 != false2,
inference(flattening,[],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ( ( ~ d(X0)
& d(X1) )
| ( d(X0)
& d(X1)
& ~ bool(X0)
& bool(X1) )
| ( X0 = false
& X1 = true ) )
=> forallprefers(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f50,plain,
! [X0,X1] :
( forallprefers(X0,X1)
| ( ( d(X0)
| ~ d(X1) )
& ( ~ d(X0)
| ~ d(X1)
| bool(X0)
| ~ bool(X1) )
& ( false != X0
| true != X1 ) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f75,plain,
? [X0] :
( false2 = phi(f7(X0))
& ! [X1] : ~ forallprefers(f7(X1),f7(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f77,plain,
! [X0] :
( ( bool(X0)
| ( false != X0
& true != X0 ) )
& ( X0 = false
| X0 = true
| ~ bool(X0) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f78,plain,
! [X0] :
( ( bool(X0)
| ( false != X0
& true != X0 ) )
& ( X0 = false
| X0 = true
| ~ bool(X0) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( prop(X0) = true
| ~ bool(X0) )
& ( bool(X0)
| true != prop(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f80,plain,
! [X0] :
( ( prop(X0) = false
| bool(X0) )
& ( ~ bool(X0)
| false != prop(X0) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f87,plain,
( false2 = phi(f7(sK6))
& ! [X1] : ~ forallprefers(f7(X1),f7(sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f75]) ).
fof(f88,plain,
! [X0] :
( false = X0
| true = X0
| ~ bool(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f89,plain,
! [X0] :
( bool(X0)
| true != X0 ),
inference(cnf_transformation,[],[f78]) ).
fof(f90,plain,
! [X0] :
( bool(X0)
| false != X0 ),
inference(cnf_transformation,[],[f78]) ).
fof(f92,plain,
true != err,
inference(cnf_transformation,[],[f2]) ).
fof(f95,plain,
d(false),
inference(cnf_transformation,[],[f3]) ).
fof(f96,plain,
d(true),
inference(cnf_transformation,[],[f3]) ).
fof(f97,plain,
! [X0,X1] :
( forallprefers(X0,X1)
| false != X0
| true != X1 ),
inference(cnf_transformation,[],[f50]) ).
fof(f103,plain,
! [X0] :
( phi(X0) = X0
| err = phi(X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f104,plain,
! [X0] :
( phi(X0) = X0
| ~ d(X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f107,plain,
! [X0] :
( true != prop(X0)
| bool(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f108,plain,
! [X0] :
( ~ bool(X0)
| true = prop(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f110,plain,
! [X0] :
( false = prop(X0)
| bool(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0] : true = lazy_impl(false,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f117,plain,
! [X0] : phi(X0) = lazy_impl(true,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f146,plain,
false = false1,
inference(cnf_transformation,[],[f38]) ).
fof(f147,plain,
! [X0] : f7(X0) = lazy_impl(prop(X0),X0),
inference(cnf_transformation,[],[f39]) ).
fof(f148,plain,
! [X1] : ~ forallprefers(f7(X1),f7(sK6)),
inference(cnf_transformation,[],[f87]) ).
fof(f149,plain,
false2 = phi(f7(sK6)),
inference(cnf_transformation,[],[f87]) ).
fof(f154,plain,
false1 != false2,
inference(cnf_transformation,[],[f47]) ).
fof(f162,plain,
! [X0] :
( bool(X0)
| false1 != X0 ),
inference(definition_unfolding,[],[f90,f146]) ).
fof(f163,plain,
! [X0] :
( ~ bool(X0)
| true = X0
| false1 = X0 ),
inference(definition_unfolding,[],[f88,f146]) ).
fof(f166,plain,
d(false1),
inference(definition_unfolding,[],[f95,f146]) ).
fof(f167,plain,
! [X0,X1] :
( forallprefers(X0,X1)
| false1 != X0
| true != X1 ),
inference(definition_unfolding,[],[f97,f146]) ).
fof(f170,plain,
! [X0] :
( ~ d(X0)
| lazy_impl(true,X0) = X0 ),
inference(definition_unfolding,[],[f104,f117]) ).
fof(f171,plain,
! [X0] :
( lazy_impl(true,X0) = X0
| err = lazy_impl(true,X0) ),
inference(definition_unfolding,[],[f103,f117,f117]) ).
fof(f172,plain,
! [X0] :
( bool(X0)
| prop(X0) = false1 ),
inference(definition_unfolding,[],[f110,f146]) ).
fof(f178,plain,
! [X0] : true = lazy_impl(false1,X0),
inference(definition_unfolding,[],[f116,f146]) ).
fof(f193,plain,
false2 = lazy_impl(true,lazy_impl(prop(sK6),sK6)),
inference(definition_unfolding,[],[f149,f117,f147]) ).
fof(f194,plain,
! [X1] : ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(sK6),sK6)),
inference(definition_unfolding,[],[f148,f147,f147]) ).
fof(f198,plain,
bool(false1),
inference(equality_resolution,[],[f162]) ).
fof(f199,plain,
bool(true),
inference(equality_resolution,[],[f89]) ).
fof(f200,plain,
! [X1] :
( forallprefers(false1,X1)
| true != X1 ),
inference(equality_resolution,[],[f167]) ).
fof(f201,plain,
forallprefers(false1,true),
inference(equality_resolution,[],[f200]) ).
fof(f204,plain,
true = prop(false1),
inference(resolution,[],[f108,f198]) ).
fof(f205,plain,
true = prop(true),
inference(resolution,[],[f108,f199]) ).
fof(f206,plain,
! [X0] :
( prop(X0) = false1
| true = prop(X0) ),
inference(resolution,[],[f172,f108]) ).
fof(f223,plain,
true = lazy_impl(true,true),
inference(resolution,[],[f170,f96]) ).
fof(f225,plain,
false1 = lazy_impl(true,false1),
inference(resolution,[],[f170,f166]) ).
fof(f275,plain,
( false2 = lazy_impl(true,lazy_impl(false1,sK6))
| true = prop(sK6) ),
inference(superposition,[],[f193,f206]) ).
fof(f278,plain,
( false2 = lazy_impl(true,true)
| true = prop(sK6) ),
inference(forward_demodulation,[],[f275,f178]) ).
fof(f279,plain,
( true = false2
| true = prop(sK6) ),
inference(forward_demodulation,[],[f278,f223]) ).
fof(f281,definition,
( spl7_1
<=> true = prop(sK6) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f283,plain,
( true = prop(sK6)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f285,definition,
( spl7_2
<=> true = false2 ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f287,plain,
( true = false2
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f279,f285,f281]) ).
fof(f307,plain,
~ forallprefers(lazy_impl(true,false1),lazy_impl(prop(sK6),sK6)),
inference(superposition,[],[f194,f204]) ).
fof(f314,plain,
~ forallprefers(false1,lazy_impl(prop(sK6),sK6)),
inference(forward_demodulation,[],[f307,f225]) ).
fof(f337,plain,
( err = false2
| false2 = lazy_impl(prop(sK6),sK6) ),
inference(superposition,[],[f171,f193]) ).
fof(f343,plain,
( true = err
| false2 = lazy_impl(prop(sK6),sK6)
| ~ spl7_2 ),
inference(forward_demodulation,[],[f337,f287]) ).
fof(f346,plain,
( false2 = lazy_impl(prop(sK6),sK6)
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f343,f92]) ).
fof(f349,plain,
( true = lazy_impl(prop(sK6),sK6)
| ~ spl7_2 ),
inference(forward_demodulation,[],[f346,f287]) ).
fof(f364,plain,
( true != true
| bool(sK6)
| ~ spl7_1 ),
inference(superposition,[],[f107,f283]) ).
fof(f365,plain,
( bool(sK6)
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f364]) ).
fof(f372,plain,
( true = sK6
| false1 = sK6
| ~ spl7_1 ),
inference(resolution,[],[f365,f163]) ).
fof(f377,definition,
( spl7_8
<=> false1 = sK6 ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
fof(f379,plain,
( false1 = sK6
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f381,definition,
( spl7_9
<=> true = sK6 ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
fof(f383,plain,
( true = sK6
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f384,plain,
( spl7_8
| spl7_9
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f372,f281,f381,f377]) ).
fof(f390,plain,
( false2 = lazy_impl(true,lazy_impl(prop(false1),false1))
| ~ spl7_8 ),
inference(superposition,[],[f193,f379]) ).
fof(f391,plain,
( false2 = lazy_impl(true,lazy_impl(true,false1))
| ~ spl7_8 ),
inference(forward_demodulation,[],[f390,f204]) ).
fof(f394,plain,
( false2 = lazy_impl(true,false1)
| ~ spl7_8 ),
inference(forward_demodulation,[],[f391,f225]) ).
fof(f397,plain,
( false1 = false2
| ~ spl7_8 ),
inference(forward_demodulation,[],[f394,f225]) ).
fof(f400,plain,
( $false
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f397,f154]) ).
fof(f401,plain,
~ spl7_8,
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f736,plain,
( ~ forallprefers(false1,lazy_impl(prop(true),true))
| ~ spl7_9 ),
inference(forward_demodulation,[],[f314,f383]) ).
fof(f737,plain,
( ~ forallprefers(false1,lazy_impl(true,true))
| ~ spl7_9 ),
inference(forward_demodulation,[],[f736,f205]) ).
fof(f738,plain,
( ~ forallprefers(false1,true)
| ~ spl7_9 ),
inference(forward_demodulation,[],[f737,f223]) ).
fof(f739,plain,
( $false
| ~ spl7_9 ),
inference(forward_subsumption_resolution,[],[f738,f201]) ).
fof(f740,plain,
~ spl7_9,
inference(avatar_contradiction_clause,[],[f739]) ).
fof(f753,plain,
( ~ forallprefers(false1,true)
| ~ spl7_2 ),
inference(forward_demodulation,[],[f314,f349]) ).
fof(f754,plain,
( $false
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f753,f201]) ).
fof(f755,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f754]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f288]) ).
cnf(s7,plain,
( ~ spl7_1
| spl7_8
| spl7_9 ),
inference(sat_conversion,[],[f384]) ).
cnf(s9,plain,
~ spl7_8,
inference(sat_conversion,[],[f401]) ).
cnf(s22,plain,
~ spl7_9,
inference(sat_conversion,[],[f740]) ).
cnf(s24,plain,
~ spl7_2,
inference(sat_conversion,[],[f755]) ).
cnf(s25,plain,
~ spl7_1,
inference(rat,[],[s7,s22,s9]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s1,s24,s25]) ).
fof(f756,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n010.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 13:12:18 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.26 % (1914541)Will run a generic schedule for satisfiability detection.
% 0.37/0.26 % (1914548)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3837170296:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.37/0.26 % (1914547)% WARNING: option uhcvi not known.
% 0.37/0.26 % (1914546)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2657973808_2999 on theBenchmark for (2999ds/0Mi)
% 0.37/0.26 % (1914547)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3660976728:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.37/0.26 % (1914549)dis+10_1_sil=32000:sp=arity:random_seed=2444057093:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.37/0.26 % (1914550)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2179290264:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.37/0.26 % (1914552)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2716349983:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.37/0.26 % (1914551)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=688203759:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.37/0.26 % Detected minimum model sizes of [3]
% 0.37/0.26 % Detected maximum model sizes of [max]
% 0.37/0.26 % TRYING [3]
% 0.37/0.26 % (1914549) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1914541-1914549"...
% 0.37/0.26 % (1914549)...printing done.
% 0.37/0.26 % TRYING [4]
% 0.37/0.26 % (1914549)Refutation found. Thanks to Tanya!
% 0.37/0.26 % SZS status Theorem for theBenchmark
% 0.37/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.27 % (1914549)------------------------------
% 0.37/0.27 % (1914549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.27 % (1914549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.27 % (1914549)CaDiCaL version: 2.1.3
% 0.37/0.27 % (1914549)Termination reason: Refutation
% 0.37/0.27 % (1914549)Time elapsed: 0.016 s
% 0.37/0.27 % (1914549)Peak memory usage: 12 MB
% 0.37/0.27 % (1914549)Instructions burned: 25 (million)
% 0.37/0.27 % (1914541)Success in time 0.054 s
% 0.37/0.27 % Vampire exiting
%------------------------------------------------------------------------------