%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX075_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 01:45:49 PM UTC 2026
% Result : Theorem 3.88s 1.33s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 128 ( 42 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 135 ( 48 ~; 41 |; 39 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 4 ( 2 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 3 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 40 !; 20 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
general: $tType ).
tff(type_def_6,type,
symbol: $tType ).
tff(func_def_0,type,
f__integer__: $int > general ).
tff(func_def_1,type,
f__symbolic__: symbol > general ).
tff(func_def_2,type,
c__infimum__: general ).
tff(func_def_3,type,
c__supremum__: general ).
tff(func_def_8,type,
sK0: ( general * general ) > general ).
tff(func_def_9,type,
sK1: ( general * general ) > general ).
tff(func_def_10,type,
sK2: ( general * general ) > general ).
tff(func_def_11,type,
sK3: ( general * general ) > general ).
tff(func_def_12,type,
sK4: general > general ).
tff(func_def_13,type,
sK5: general > general ).
tff(func_def_14,type,
sK6: general > general ).
tff(func_def_15,type,
sK7: general > general ).
tff(func_def_16,type,
sK8: general > general ).
tff(func_def_17,type,
sK9: general > general ).
tff(func_def_18,type,
sK10: general ).
tff(func_def_19,type,
sK11: general ).
tff(pred_def_1,type,
p__is_integer__: general > $o ).
tff(pred_def_2,type,
p__is_symbolic__: general > $o ).
tff(pred_def_3,type,
p__less_equal__: ( general * general ) > $o ).
tff(pred_def_4,type,
p__less__: ( general * general ) > $o ).
tff(pred_def_5,type,
p__greater_equal__: ( general * general ) > $o ).
tff(pred_def_6,type,
p__greater__: ( general * general ) > $o ).
tff(pred_def_8,type,
edge: ( general * general ) > $o ).
tff(pred_def_9,type,
vertex: general > $o ).
tff(pred_def_10,type,
aux: general > $o ).
tff(pred_def_11,type,
color: general > $o ).
tff(pred_def_12,type,
color: ( general * general ) > $o ).
tff(f21,axiom,
! [X0: general,X1: general] :
( color(X0,X1)
<=> ? [X2: general,X3: general] :
( ( X0 = X2 )
& ? [X4: general] :
( color(X4)
& ( X4 = X3 ) )
& ( X1 = X3 )
& ? [X3: general] :
( ( X3 = X2 )
& vertex(X3) )
& color(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_5_completed_definition_of_color_2) ).
tff(f22,conjecture,
! [X1: general,X0: general] :
( color(X0,X1)
=> ( color(X1)
& vertex(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_6_unnamed_formula) ).
tff(f23,negated_conjecture,
~ ! [X1: general,X0: general] :
( color(X0,X1)
=> ( color(X1)
& vertex(X0) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
tff(f37,plain,
~ ! [X1: general,X0: general] :
( color(X1,X0)
=> ( vertex(X1)
& color(X0) ) ),
inference(rectify,[],[f23]) ).
tff(f40,plain,
! [X0: general,X1: general] :
( ? [X2: general,X3: general] :
( color(X0,X1)
& ( X1 = X3 )
& ? [X5: general] :
( vertex(X5)
& ( X2 = X5 ) )
& ? [X4: general] :
( color(X4)
& ( X4 = X3 ) )
& ( X0 = X2 ) )
<=> color(X0,X1) ),
inference(rectify,[],[f21]) ).
tff(f50,plain,
? [X1: general,X0: general] :
( color(X1,X0)
& ( ~ vertex(X1)
| ~ color(X0) ) ),
inference(ennf_transformation,[],[f37]) ).
tff(f54,plain,
! [X0: general,X1: general] :
( ( ? [X2: general,X3: general] :
( color(X0,X1)
& ( X1 = X3 )
& ? [X5: general] :
( vertex(X5)
& ( X2 = X5 ) )
& ? [X4: general] :
( color(X4)
& ( X4 = X3 ) )
& ( X0 = X2 ) )
| ~ color(X0,X1) )
& ( color(X0,X1)
| ! [X2: general,X3: general] :
( ~ color(X0,X1)
| ( X1 != X3 )
| ! [X5: general] :
( ~ vertex(X5)
| ( X2 != X5 ) )
| ! [X4: general] :
( ~ color(X4)
| ( X3 != X4 ) )
| ( X0 != X2 ) ) ) ),
inference(nnf_transformation,[],[f40]) ).
tff(f55,plain,
! [X0: general,X1: general] :
( ( ? [X2: general,X3: general] :
( color(X0,X1)
& ( X1 = X3 )
& ? [X4: general] :
( vertex(X4)
& ( X2 = X4 ) )
& ? [X5: general] :
( color(X5)
& ( X3 = X5 ) )
& ( X0 = X2 ) )
| ~ color(X0,X1) )
& ( color(X0,X1)
| ! [X6: general,X7: general] :
( ~ color(X0,X1)
| ( X1 != X7 )
| ! [X8: general] :
( ~ vertex(X8)
| ( X6 != X8 ) )
| ! [X9: general] :
( ~ color(X9)
| ( X7 != X9 ) )
| ( X0 != X6 ) ) ) ),
inference(rectify,[],[f54]) ).
tff(f56,plain,
! [X0: general,X1: general] :
( ( ( color(X0,X1)
& ( sK1(X0,X1) = X1 )
& vertex(sK2(X0,X1))
& ( sK2(X0,X1) = sK0(X0,X1) )
& color(sK3(X0,X1))
& ( sK3(X0,X1) = sK1(X0,X1) )
& ( sK0(X0,X1) = X0 ) )
| ~ color(X0,X1) )
& ( color(X0,X1)
| ! [X6: general,X7: general] :
( ~ color(X0,X1)
| ( X1 != X7 )
| ! [X8: general] :
( ~ vertex(X8)
| ( X6 != X8 ) )
| ! [X9: general] :
( ~ color(X9)
| ( X7 != X9 ) )
| ( X0 != X6 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X5,sK3(X0,X1))],[f55]) ).
tff(f60,plain,
? [X0: general,X1: general] :
( color(X0,X1)
& ( ~ vertex(X0)
| ~ color(X1) ) ),
inference(rectify,[],[f50]) ).
tff(f61,plain,
( color(sK10,sK11)
& ( ~ vertex(sK10)
| ~ color(sK11) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f60]) ).
tff(f63,plain,
! [X0: general,X1: general] :
( ~ color(X0,X1)
| ( sK0(X0,X1) = X0 ) ),
inference(cnf_transformation,[],[f56]) ).
tff(f64,plain,
! [X0: general,X1: general] :
( ~ color(X0,X1)
| ( sK3(X0,X1) = sK1(X0,X1) ) ),
inference(cnf_transformation,[],[f56]) ).
tff(f65,plain,
! [X0: general,X1: general] :
( color(sK3(X0,X1))
| ~ color(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tff(f66,plain,
! [X0: general,X1: general] :
( ~ color(X0,X1)
| ( sK2(X0,X1) = sK0(X0,X1) ) ),
inference(cnf_transformation,[],[f56]) ).
tff(f67,plain,
! [X0: general,X1: general] :
( vertex(sK2(X0,X1))
| ~ color(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tff(f68,plain,
! [X0: general,X1: general] :
( ~ color(X0,X1)
| ( sK1(X0,X1) = X1 ) ),
inference(cnf_transformation,[],[f56]) ).
tff(f79,plain,
( ~ vertex(sK10)
| ~ color(sK11) ),
inference(cnf_transformation,[],[f61]) ).
tff(f80,plain,
color(sK10,sK11),
inference(cnf_transformation,[],[f61]) ).
tff(f95,definition,
( spl12_1
<=> vertex(sK10) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
tff(f97,plain,
( ~ vertex(sK10)
| spl12_1 ),
inference(avatar_component_clause,[],[f95]) ).
tff(f99,definition,
( spl12_2
<=> color(sK11) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
tff(f102,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f79,f99,f95]) ).
tff(f117,plain,
sK10 = sK0(sK10,sK11),
inference(resolution,[],[f63,f80]) ).
tff(f118,plain,
sK11 = sK1(sK10,sK11),
inference(resolution,[],[f68,f80]) ).
tff(f122,plain,
sK3(sK10,sK11) = sK1(sK10,sK11),
inference(resolution,[],[f64,f80]) ).
tff(f123,plain,
sK3(sK10,sK11) = sK11,
inference(forward_demodulation,[],[f122,f118]) ).
tff(f124,plain,
( ~ color(sK10,sK11)
| color(sK11) ),
inference(superposition,[],[f65,f123]) ).
tff(f125,plain,
color(sK11),
inference(forward_subsumption_resolution,[],[f124,f80]) ).
tff(f126,plain,
spl12_2,
inference(avatar_split_clause,[],[f125,f99]) ).
tff(f128,plain,
sK2(sK10,sK11) = sK0(sK10,sK11),
inference(resolution,[],[f66,f80]) ).
tff(f129,plain,
sK2(sK10,sK11) = sK10,
inference(forward_demodulation,[],[f128,f117]) ).
tff(f131,plain,
( vertex(sK10)
| ~ color(sK10,sK11) ),
inference(superposition,[],[f67,f129]) ).
tff(f132,plain,
( ~ color(sK10,sK11)
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f131,f97]) ).
tff(f134,plain,
( $false
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f132,f80]) ).
tff(f135,plain,
spl12_1,
inference(avatar_contradiction_clause,[],[f134]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f102]) ).
cnf(s2,plain,
spl12_2,
inference(sat_conversion,[],[f126]) ).
cnf(s3,plain,
spl12_1,
inference(sat_conversion,[],[f135]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
tff(f136,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX075_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:59:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.88/1.33 % (1245491)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.88/1.33 % (1245500)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1547451988:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.88/1.33 % (1245500)Instruction limit reached!
% 3.88/1.33 % (1245500)------------------------------
% 3.88/1.33 % (1245500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (1245500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (1245500)CaDiCaL version: 2.1.3
% 3.88/1.33 % (1245500)Termination reason: Instruction limit
% 3.88/1.33 % (1245500)Termination phase: Saturation
% 3.88/1.33 % (1245500)Time elapsed: 0.003 s
% 3.88/1.33 % (1245500)Peak memory usage: 89 MB
% 3.88/1.33 % (1245500)Instructions burned: 7 (million)
% 3.88/1.33 % (1245499)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2741900234:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.88/1.33 % (1245497)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2300207430:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.88/1.33 % (1245498)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2753796008:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.88/1.33 % (1245496)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=688627932:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.88/1.33 % (1245499)Instruction limit reached!
% 3.88/1.33 % (1245499)------------------------------
% 3.88/1.33 % (1245499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (1245499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (1245499)CaDiCaL version: 2.1.3
% 3.88/1.33 % (1245499)Termination reason: Instruction limit
% 3.88/1.33 % (1245499)Termination phase: Saturation
% 3.88/1.33 % (1245499)Time elapsed: 0.007 s
% 3.88/1.33 % (1245499)Peak memory usage: 88 MB
% 3.88/1.33 % (1245499)Instructions burned: 8 (million)
% 3.88/1.33 % (1245501)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=151354980:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.88/1.33 % (1245502)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2735827476:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.88/1.33 % (1245496)Refutation not found, incomplete strategy
% 3.88/1.33 % (1245496)------------------------------
% 3.88/1.33 % (1245496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (1245496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (1245496)CaDiCaL version: 2.1.3
% 3.88/1.33 % (1245496)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.33 % (1245496)Time elapsed: 0.031 s
% 3.88/1.33 % (1245496)Peak memory usage: 115 MB
% 3.88/1.33 % (1245496)Instructions burned: 7 (million)
% 3.88/1.33 % (1245498)First to succeed.
% 3.88/1.33 % (1245498)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1245491"
% 3.88/1.33 % (1245497)Also succeeded, but the first one will report.
% 3.88/1.33 % (1245501)Also succeeded, but the first one will report.
% 3.88/1.33 % (1245502)Also succeeded, but the first one will report.
% 3.88/1.33 % (1245504)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1105147365:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.88/1.33 % (1245504)Also succeeded, but the first one will report.
% 3.88/1.33 % (1245509)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=4005703049:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.88/1.33 % (1245509)Also succeeded, but the first one will report.
% 3.88/1.33 % (1245496)------------------------------
% 3.88/1.33 % (1245496)------------------------------
% 3.88/1.33 % (1245498)Refutation found. Thanks to Tanya!
% 3.88/1.33 % SZS status Theorem for theBenchmark
% 3.88/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.33 % (1245498)------------------------------
% 3.88/1.33 % (1245498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (1245498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (1245498)CaDiCaL version: 2.1.3
% 3.88/1.33 % (1245498)Termination reason: Refutation
% 3.88/1.33 % (1245498)Time elapsed: 0.032 s
% 3.88/1.33 % (1245498)Peak memory usage: 113 MB
% 3.88/1.33 % (1245498)Instructions burned: 10 (million)
% 3.88/1.33 % (1245498)------------------------------
% 3.88/1.33 % (1245498)------------------------------
% 3.88/1.33 % (1245491)Success in time 0.46 s
% 3.88/1.33 % Vampire exiting
%------------------------------------------------------------------------------