%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX074_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 : n019.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 0.77s 0.95s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 10 unt; 0 typ; 7 def)
% Number of atoms : 264 ( 74 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 299 ( 101 ~; 100 |; 82 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 19 ( 17 usr; 7 prp; 0-2 aty)
% Number of functors : 11 ( 10 usr; 5 con; 0-1 aty)
% Number of variables : 80 ( 0 sgn 50 !; 30 ?; 80 :)
% 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,
sK1: general > symbol ).
tff(func_def_9,type,
sK2: general > general ).
tff(func_def_10,type,
sK3: general ).
tff(func_def_11,type,
sK4: general ).
tff(func_def_12,type,
sK5: general ).
tff(func_def_13,type,
sK6: general > $int ).
tff(func_def_17,type,
-1: $int > $int ).
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,
hq: general > $o ).
tff(pred_def_9,type,
tq: general > $o ).
tff(pred_def_10,type,
hp: general > $o ).
tff(pred_def_11,type,
tp: general > $o ).
tff(pred_def_13,type,
sP0: ( general * general ) > $o ).
tff(f18,axiom,
! [X0: general,X1: general] :
( ( ( ( X0 = X1 )
& ? [X2: general] :
( ( X2 = X1 )
& hp(X2) )
& ? [X2: general] :
( ( X2 = X1 )
& tq(X2) ) )
=> hq(X0) )
& ( ( ( X0 = X1 )
& ? [X2: general] :
( tp(X2)
& ( X2 = X1 ) )
& ? [X2: general] :
( ( X2 = X1 )
& tq(X2) ) )
=> tq(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_2_right_0) ).
tff(f19,conjecture,
! [X1: general,X0: general] :
( ( ( ? [X2: general] :
( tp(X2)
& ( X2 = X1 ) )
& tq(X0)
& ( X0 = X1 ) )
=> tq(X0) )
& ( ( ? [X2: general] :
( ( X2 = X1 )
& hp(X2) )
& ( X0 = X1 )
& tq(X0) )
=> hq(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_3_left_0) ).
tff(f20,negated_conjecture,
~ ! [X1: general,X0: general] :
( ( ( ? [X2: general] :
( tp(X2)
& ( X2 = X1 ) )
& tq(X0)
& ( X0 = X1 ) )
=> tq(X0) )
& ( ( ? [X2: general] :
( ( X2 = X1 )
& hp(X2) )
& ( X0 = X1 )
& tq(X0) )
=> hq(X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
tff(f34,plain,
~ ! [X0: general,X1: general] :
( ( ( ? [X2: general] :
( ( X0 = X2 )
& tp(X2) )
& ( X0 = X1 )
& tq(X1) )
=> tq(X1) )
& ( ( tq(X1)
& ? [X3: general] :
( ( X0 = X3 )
& hp(X3) )
& ( X0 = X1 ) )
=> hq(X1) ) ),
inference(rectify,[],[f20]) ).
tff(f39,plain,
! [X0: general,X1: general] :
( ( ( ( X0 = X1 )
& ? [X3: general] :
( tq(X3)
& ( X1 = X3 ) )
& ? [X2: general] :
( ( X2 = X1 )
& hp(X2) ) )
=> hq(X0) )
& ( ( ? [X5: general] :
( tq(X5)
& ( X1 = X5 ) )
& ( X0 = X1 )
& ? [X4: general] :
( tp(X4)
& ( X1 = X4 ) ) )
=> tq(X0) ) ),
inference(rectify,[],[f18]) ).
tff(f44,plain,
! [X0: general,X1: general] :
( ( hq(X0)
| ( X0 != X1 )
| ! [X3: general] :
( ( X1 != X3 )
| ~ tq(X3) )
| ! [X2: general] :
( ( X1 != X2 )
| ~ hp(X2) ) )
& ( tq(X0)
| ! [X5: general] :
( ( X1 != X5 )
| ~ tq(X5) )
| ( X0 != X1 )
| ! [X4: general] :
( ~ tp(X4)
| ( X1 != X4 ) ) ) ),
inference(ennf_transformation,[],[f39]) ).
tff(f45,plain,
! [X0: general,X1: general] :
( ( tq(X0)
| ! [X5: general] :
( ( X1 != X5 )
| ~ tq(X5) )
| ! [X4: general] :
( ~ tp(X4)
| ( X1 != X4 ) )
| ( X0 != X1 ) )
& ( ( X0 != X1 )
| hq(X0)
| ! [X3: general] :
( ( X1 != X3 )
| ~ tq(X3) )
| ! [X2: general] :
( ( X1 != X2 )
| ~ hp(X2) ) ) ),
inference(flattening,[],[f44]) ).
tff(f55,plain,
? [X0: general,X1: general] :
( ( ~ tq(X1)
& ? [X2: general] :
( ( X0 = X2 )
& tp(X2) )
& ( X0 = X1 )
& tq(X1) )
| ( ~ hq(X1)
& tq(X1)
& ? [X3: general] :
( ( X0 = X3 )
& hp(X3) )
& ( X0 = X1 ) ) ),
inference(ennf_transformation,[],[f34]) ).
tff(f56,plain,
? [X0: general,X1: general] :
( ( ( X0 = X1 )
& ~ hq(X1)
& ? [X3: general] :
( ( X0 = X3 )
& hp(X3) )
& tq(X1) )
| ( ? [X2: general] :
( ( X0 = X2 )
& tp(X2) )
& ~ tq(X1)
& ( X0 = X1 )
& tq(X1) ) ),
inference(flattening,[],[f55]) ).
tff(f57,definition,
! [X0: general,X1: general] :
( ( ? [X2: general] :
( ( X0 = X2 )
& tp(X2) )
& ~ tq(X1)
& ( X0 = X1 )
& tq(X1) )
| ~ sP0(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f58,plain,
? [X0: general,X1: general] :
( ( ( X0 = X1 )
& ~ hq(X1)
& ? [X3: general] :
( ( X0 = X3 )
& hp(X3) )
& tq(X1) )
| sP0(X0,X1) ),
inference(definition_folding,[],[f56,f57]) ).
tff(f62,plain,
! [X0: general,X1: general] :
( ( tq(X0)
| ! [X2: general] :
( ( X1 != X2 )
| ~ tq(X2) )
| ! [X3: general] :
( ~ tp(X3)
| ( X1 != X3 ) )
| ( X0 != X1 ) )
& ( ( X0 != X1 )
| hq(X0)
| ! [X4: general] :
( ( X1 != X4 )
| ~ tq(X4) )
| ! [X5: general] :
( ( X1 != X5 )
| ~ hp(X5) ) ) ),
inference(rectify,[],[f45]) ).
tff(f65,plain,
! [X0: general,X1: general] :
( ( ? [X2: general] :
( ( X0 = X2 )
& tp(X2) )
& ~ tq(X1)
& ( X0 = X1 )
& tq(X1) )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f57]) ).
tff(f66,plain,
! [X0: general,X1: general] :
( ( ( sK2(X0) = X0 )
& tp(sK2(X0))
& ~ tq(X1)
& ( X0 = X1 )
& tq(X1) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0))],[f65]) ).
tff(f67,plain,
? [X0: general,X1: general] :
( ( ( X0 = X1 )
& ~ hq(X1)
& ? [X2: general] :
( ( X0 = X2 )
& hp(X2) )
& tq(X1) )
| sP0(X0,X1) ),
inference(rectify,[],[f58]) ).
tff(f68,plain,
( ( ( sK4 = sK3 )
& ~ hq(sK4)
& ( sK5 = sK3 )
& hp(sK5)
& tq(sK4) )
| sP0(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f67]) ).
tff(f79,plain,
! [X0: general,X1: general,X4: general,X5: general] :
( ( X0 != X1 )
| hq(X0)
| ( X1 != X4 )
| ~ tq(X4)
| ( X1 != X5 )
| ~ hp(X5) ),
inference(cnf_transformation,[],[f62]) ).
tff(f88,plain,
! [X0: general,X1: general] :
( ~ sP0(X0,X1)
| tq(X1) ),
inference(cnf_transformation,[],[f66]) ).
tff(f90,plain,
! [X0: general,X1: general] :
( ~ sP0(X0,X1)
| ~ tq(X1) ),
inference(cnf_transformation,[],[f66]) ).
tff(f93,plain,
( tq(sK4)
| sP0(sK3,sK4) ),
inference(cnf_transformation,[],[f68]) ).
tff(f94,plain,
( hp(sK5)
| sP0(sK3,sK4) ),
inference(cnf_transformation,[],[f68]) ).
tff(f95,plain,
( ( sK5 = sK3 )
| sP0(sK3,sK4) ),
inference(cnf_transformation,[],[f68]) ).
tff(f96,plain,
( ~ hq(sK4)
| sP0(sK3,sK4) ),
inference(cnf_transformation,[],[f68]) ).
tff(f97,plain,
( sP0(sK3,sK4)
| ( sK4 = sK3 ) ),
inference(cnf_transformation,[],[f68]) ).
tff(f110,plain,
! [X1: general,X4: general,X5: general] :
( hq(X1)
| ( X1 != X4 )
| ~ tq(X4)
| ( X1 != X5 )
| ~ hp(X5) ),
inference(equality_resolution,[],[f79]) ).
tff(f111,plain,
! [X4: general,X5: general] :
( hq(X4)
| ~ tq(X4)
| ( X4 != X5 )
| ~ hp(X5) ),
inference(equality_resolution,[],[f110]) ).
tff(f112,plain,
! [X5: general] :
( ~ hp(X5)
| hq(X5)
| ~ tq(X5) ),
inference(equality_resolution,[],[f111]) ).
tff(f116,definition,
( spl7_1
<=> sP0(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f118,plain,
( sP0(sK3,sK4)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f116]) ).
tff(f120,definition,
( spl7_2
<=> ( sK5 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f122,plain,
( ( sK5 = sK3 )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f120]) ).
tff(f123,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f95,f120,f116]) ).
tff(f125,definition,
( spl7_3
<=> tq(sK4) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
tff(f128,plain,
( spl7_3
| spl7_1 ),
inference(avatar_split_clause,[],[f93,f116,f125]) ).
tff(f130,definition,
( spl7_4
<=> ( sK4 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f132,plain,
( ( sK4 = sK3 )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f130]) ).
tff(f133,plain,
( spl7_1
| spl7_4 ),
inference(avatar_split_clause,[],[f97,f130,f116]) ).
tff(f135,definition,
( spl7_5
<=> hq(sK4) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
tff(f137,plain,
( ~ hq(sK4)
| spl7_5 ),
inference(avatar_component_clause,[],[f135]) ).
tff(f138,plain,
( ~ spl7_5
| spl7_1 ),
inference(avatar_split_clause,[],[f96,f116,f135]) ).
tff(f140,definition,
( spl7_6
<=> hp(sK5) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
tff(f142,plain,
( hp(sK5)
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f140]) ).
tff(f143,plain,
( spl7_1
| spl7_6 ),
inference(avatar_split_clause,[],[f94,f140,f116]) ).
tff(f144,plain,
( hp(sK3)
| ~ spl7_2
| ~ spl7_6 ),
inference(constrained_superposition,[],[f142,f122]) ).
tff(f154,plain,
! [X0: general,X1: general] : ~ sP0(X0,X1),
inference(forward_subsumption_resolution,[],[f90,f88]) ).
tff(f168,plain,
( hq(sK3)
| ~ tq(sK3)
| ~ spl7_2
| ~ spl7_6 ),
inference(resolution,[],[f112,f144]) ).
tff(f170,plain,
( hq(sK4)
| ~ tq(sK3)
| ~ spl7_2
| ~ spl7_4
| ~ spl7_6 ),
inference(forward_demodulation,[],[f168,f132]) ).
tff(f173,plain,
( ~ tq(sK3)
| ~ spl7_2
| ~ spl7_4
| spl7_5
| ~ spl7_6 ),
inference(forward_subsumption_resolution,[],[f170,f137]) ).
tff(f177,plain,
( ~ tq(sK4)
| ~ spl7_2
| ~ spl7_4
| spl7_5
| ~ spl7_6 ),
inference(forward_demodulation,[],[f173,f132]) ).
tff(f185,plain,
( $false
| ~ spl7_1 ),
inference(forward_subsumption_resolution,[],[f118,f154]) ).
tff(f186,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f185]) ).
tff(f189,plain,
( ~ spl7_3
| ~ spl7_2
| ~ spl7_4
| spl7_5
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f177,f140,f135,f130,f120,f125]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f128]) ).
cnf(s3,plain,
( spl7_1
| spl7_4 ),
inference(sat_conversion,[],[f133]) ).
cnf(s4,plain,
( spl7_1
| ~ spl7_5 ),
inference(sat_conversion,[],[f138]) ).
cnf(s5,plain,
( spl7_1
| spl7_6 ),
inference(sat_conversion,[],[f143]) ).
cnf(s9,plain,
~ spl7_1,
inference(sat_conversion,[],[f186]) ).
cnf(s10,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4
| spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f189]) ).
cnf(s13,plain,
spl7_6,
inference(rat,[],[s5,s9]) ).
cnf(s14,plain,
~ spl7_5,
inference(rat,[],[s4,s9]) ).
cnf(s15,plain,
spl7_4,
inference(rat,[],[s3,s9]) ).
cnf(s16,plain,
spl7_3,
inference(rat,[],[s2,s9]) ).
cnf(s17,plain,
~ spl7_2,
inference(rat,[],[s10,s13,s14,s15,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s17,s9]) ).
tff(f192,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX074_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.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 15:00:18 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.77/0.95 % (4065320)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.77/0.95 % (4065329)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2180640470:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.77/0.95 % (4065329)First to succeed.
% 0.77/0.95 % (4065329)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4065320"
% 0.77/0.95 % (4065325)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3328365024:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.77/0.95 % (4065326)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2613273190:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.77/0.95 % (4065328)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=218695437:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.77/0.95 % (4065327)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1295130620:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.77/0.95 % (4065328)Instruction limit reached!
% 0.77/0.95 % (4065328)------------------------------
% 0.77/0.95 % (4065328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/0.95 % (4065328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.95 % (4065328)CaDiCaL version: 2.1.3
% 0.77/0.95 % (4065328)Termination reason: Instruction limit
% 0.77/0.95 % (4065328)Termination phase: Saturation
% 0.77/0.95 % (4065328)Time elapsed: 0.006 s
% 0.77/0.95 % (4065328)Peak memory usage: 88 MB
% 0.77/0.95 % (4065328)Instructions burned: 7 (million)
% 0.77/0.95 % (4065331)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1680957970:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.77/0.95 % (4065330)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1521228741:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.77/0.95 % (4065325)Refutation not found, incomplete strategy
% 0.77/0.95 % (4065325)------------------------------
% 0.77/0.95 % (4065325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/0.95 % (4065325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.95 % (4065325)CaDiCaL version: 2.1.3
% 0.77/0.95 % (4065325)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.95 % (4065325)Time elapsed: 0.034 s
% 0.77/0.95 % (4065325)Peak memory usage: 116 MB
% 0.77/0.95 % (4065325)Instructions burned: 12 (million)
% 0.77/0.95 % (4065327)Also succeeded, but the first one will report.
% 0.77/0.95 % (4065326)Also succeeded, but the first one will report.
% 0.77/0.95 % (4065330)Also succeeded, but the first one will report.
% 0.77/0.95 % (4065331)Also succeeded, but the first one will report.
% 0.77/0.95 % (4065329)Refutation found. Thanks to Tanya!
% 0.77/0.95 % SZS status Theorem for theBenchmark
% 0.77/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.13 % (4065329)------------------------------
% 0.19/1.13 % (4065329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.13 % (4065329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.13 % (4065329)CaDiCaL version: 2.1.3
% 0.19/1.13 % (4065329)Termination reason: Refutation
% 0.19/1.13 % (4065329)Time elapsed: 0.003 s
% 0.19/1.13 % (4065329)Peak memory usage: 90 MB
% 0.19/1.13 % (4065329)Instructions burned: 5 (million)
% 0.19/1.13 % (4065329)------------------------------
% 0.19/1.13 % (4065329)------------------------------
% 0.19/1.13 % (4065320)Success in time 0.285 s
% 0.19/1.13 % Vampire exiting
%------------------------------------------------------------------------------