%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET630^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:23:45 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 198 ( 39 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 251 ( 40 ~; 16 |; 43 &; 147 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 4 con; 0-4 aty)
% ( 0 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 58 ( 46 ^; 8 !; 4 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(f7,axiom,
( excl_union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',excl_union) ).
thf(f8,axiom,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',intersection) ).
thf(f14,axiom,
( misses
= ( ^ [X0: $i > $o,X1: $i > $o] :
~ ? [X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',misses) ).
thf(f15,conjecture,
! [X0: $i > $o,X1: $i > $o] : ( misses @ ( intersection @ X0 @ X1 ) @ ( excl_union @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $o] : ( misses @ ( intersection @ X0 @ X1 ) @ ( excl_union @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f24,plain,
( excl_union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f25,plain,
( excl_union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f27,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f37,plain,
( misses
= ( ^ [X0: $i > $o,X1: $i > $o] :
~ ? [X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f38,plain,
( misses
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
~ ! [X0: $i > $o,X1: $i > $o] : ( misses @ ( intersection @ X0 @ X1 ) @ ( excl_union @ X0 @ X1 ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ( misses @ ( intersection @ X0 @ X1 ) @ ( excl_union @ X0 @ X1 ) )
= $true ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
? [X0: $i > $o,X1: $i > $o] :
( ( misses @ ( intersection @ X0 @ X1 ) @ ( excl_union @ X0 @ X1 ) )
!= $true ),
inference(ennf_transformation,[],[f40]) ).
thf(f42,plain,
( $true
!= ( misses @ ( intersection @ sK0 @ sK1 ) @ ( excl_union @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f41]) ).
thf(f49,plain,
( excl_union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f50,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f56,plain,
( misses
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f57,plain,
( $true
!= ( misses @ ( intersection @ sK0 @ sK1 ) @ ( excl_union @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f61,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK0
@ sK1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
| ( ~ ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f57,f56,f50,f49]) ).
thf(f62,plain,
( $true
!= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 )
& ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 )
& ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 )
& ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( $true
= ( ( sK0 @ sK2 )
& ( sK1 @ sK2 )
& ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ~ ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( $true
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ~ ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( $true
= ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f70,plain,
( ( $true
= ( ~ ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f72,plain,
( ( $true
= ( ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $true
= ( ~ ( sK1 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f76,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f74]) ).
thf(f83,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(forward_demodulation,[],[f76,f69]) ).
thf(f84,plain,
( $false
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f86,plain,
$false = $true,
inference(constrained_superposition,[],[f68,f84]) ).
thf(f87,plain,
$false,
inference(trivial_inequality_removal,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET630^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n008.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 13:40:39 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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 % (3166487)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (3166493)% WARNING: option uhcvi not known.
% 0.20/0.28 % (3166493)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2220633567:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (3166492)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1302579893_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (3166494)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2963637075:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (3166493)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (3166493)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 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 % (3166494) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3166487-3166494"...
% 0.20/0.28 % (3166493) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3166487-3166493"...
% 0.20/0.28 % (3166494)...printing done.
% 0.20/0.28 % (3166493)...printing done.
% 0.20/0.28 % (3166494)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 % (3166494)------------------------------
% 0.20/0.28 % (3166494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3166494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3166494)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3166494)Termination reason: Refutation
% 0.20/0.28 % (3166494)Time elapsed: 0.004 s
% 0.20/0.28 % (3166494)Peak memory usage: 12 MB
% 0.20/0.28 % (3166494)Instructions burned: 5 (million)
% 0.20/0.28 % (3166487)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------