%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM739^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 : Wed Sep 30 08:19:25 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 329 ( 90 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 390 ( 79 ~; 51 |; 1 &; 230 @)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: frac ).
thf(func_def_1,type,
y: frac ).
thf(func_def_2,type,
z: frac ).
thf(func_def_3,type,
u: frac ).
thf(func_def_4,type,
moref: frac > frac > $o ).
thf(func_def_5,type,
eq: frac > frac > $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
eq @ x @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(f3,axiom,
eq @ y @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f) ).
thf(f5,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(f6,axiom,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz38) ).
thf(f7,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44) ).
thf(f8,conjecture,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz46) ).
thf(f9,negated_conjecture,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
eq @ x @ z,
inference(rectify,[],[f2]) ).
thf(f13,plain,
( ( eq @ x @ z )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
eq @ y @ u,
inference(rectify,[],[f3]) ).
thf(f15,plain,
( ( eq @ y @ u )
= $true ),
inference(fool_elimination,[],[f14]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
inference(rectify,[],[f5]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X1 @ X2 )
= $true )
=> ( ( eq @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
inference(rectify,[],[f6]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( eq @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f23,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X0 @ X2 )
= $true )
=> ( ( ( eq @ X1 @ X3 )
= $true )
=> ( ( moref @ X2 @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(rectify,[],[f9]) ).
thf(f25,plain,
~ ( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[],[f11]) ).
thf(f28,plain,
~ ( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(flattening,[],[f25]) ).
thf(f29,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f31,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f32,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f31]) ).
thf(f33,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f34]) ).
thf(f36,plain,
( ( ( eq @ z @ u )
!= $true )
& ( ( moref @ z @ u )
!= $true ) ),
inference(ennf_transformation,[],[f28]) ).
thf(f37,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f38,plain,
( ( eq @ x @ z )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f39,plain,
( ( eq @ y @ u )
= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f41,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f42,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f43,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f44,plain,
( ( moref @ z @ u )
!= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f45,plain,
( ( eq @ z @ u )
!= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f50,definition,
( spl0_1
<=> ( ( moref @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f52,plain,
( ( ( moref @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f54,definition,
( spl0_2
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f56,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f57,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f37,f54,f50]) ).
thf(f99,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( $true
= ( eq @ X0 @ y ) )
| ( $true
!= ( eq @ X0 @ x ) ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f41,f56]) ).
thf(f100,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
= ( eq @ X0 @ u ) )
| ( $true
!= ( eq @ X0 @ y ) ) ),
inference(constrained_superposition,[],[f41,f39]) ).
thf(f119,plain,
! [X0: frac] :
( ( $true
= ( eq @ X0 @ u ) )
| ( $true
!= ( eq @ X0 @ y ) ) ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f120,plain,
( ! [X0: frac] :
( ( $true
= ( eq @ X0 @ y ) )
| ( $true
!= ( eq @ X0 @ x ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f162,plain,
! [X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ X0 @ u ) )
| ( $true
!= ( eq @ X1 @ z ) )
| ( $true
!= ( moref @ X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f44,f43]) ).
thf(f163,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ u ) )
| ( $true
!= ( moref @ X1 @ X0 ) )
| ( $true
!= ( eq @ X1 @ z ) ) ),
inference(trivial_inequality_removal,[],[f162]) ).
thf(f217,plain,
( ( $true != $true )
| ( $true
!= ( eq @ z @ y ) ) ),
inference(constrained_superposition,[],[f45,f119]) ).
thf(f218,plain,
( $true
!= ( eq @ z @ y ) ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f246,plain,
( ( $true != $true )
| ( $true
!= ( eq @ z @ x ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f218,f120]) ).
thf(f247,plain,
( ( $true
!= ( eq @ z @ x ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f296,plain,
( ( $true != $true )
| ( ( eq @ x @ z )
!= $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f247,f42]) ).
thf(f297,plain,
( ( ( eq @ x @ z )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f301,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f297,f38]) ).
thf(f302,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f301]) ).
thf(f304,plain,
( ( $true != $true )
| ( ( eq @ y @ u )
!= $true )
| ( ( eq @ x @ z )
!= $true )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f163,f52]) ).
thf(f307,plain,
( ( ( eq @ y @ u )
!= $true )
| ( ( eq @ x @ z )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f308,plain,
( ( ( eq @ x @ z )
!= $true )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f307,f39]) ).
thf(f309,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f308,f38]) ).
thf(f310,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f309]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f302]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f310]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f311,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM739^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 12:47:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.28 % (704889)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (704896)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2794331858:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (704895)% WARNING: option uhcvi not known.
% 0.20/0.28 % (704897)dis+10_1_sil=32000:sp=arity:random_seed=369035334:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (704895)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2141772127:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (704894)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1163280346_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (704898)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3301111779:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (704895)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (704895)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (704900)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=695645635:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (704898)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (704898) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-704889-704898"...
% 0.20/0.28 % (704898)...printing done.
% 0.20/0.28 % (704898)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (704898)------------------------------
% 0.20/0.28 % (704898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (704898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (704898)CaDiCaL version: 2.1.3
% 0.20/0.28 % (704898)Termination reason: Refutation
% 0.20/0.28 % (704898)Time elapsed: 0.013 s
% 0.20/0.28 % (704898)Peak memory usage: 12 MB
% 0.20/0.28 % (704898)Instructions burned: 23 (million)
% 0.20/0.28 % (704889)Success in time 0.048 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------