%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP010^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:10:03 AM UTC 2026
% Result : Theorem 0.29s 0.39s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 127 ( 24 ~; 4 |; 0 &; 96 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 4 con; 0-4 aty)
% Number of variables : 20 ( 0 ^; 16 !; 4 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
thf(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
sK6: $tType ).
thf(type_def_9,type,
sK7: $tType ).
thf(func_def_0,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_2,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_4,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
c_2Ebool_2EF: $o ).
thf(func_def_6,type,
c_2Ebool_2ET: $o ).
thf(func_def_7,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_8,type,
c_2Ecardinal_2Ecardleq:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > ( X1 > $o ) > $o ) ).
thf(func_def_9,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_14,type,
vOR: $o > $o > $o ).
thf(func_def_15,type,
sP0: $o > $o > $o > $o ).
thf(func_def_16,type,
sP1: $o > $o > $o > $o ).
thf(func_def_17,type,
sP2: $o > $o > $o > $o ).
thf(func_def_18,type,
sP3: $o > $o > $o > $o ).
thf(func_def_19,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_20,type,
sK5:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_21,type,
sK8: sK6 > $o ).
thf(func_def_22,type,
sK9: sK7 > $o ).
thf(f23,conjecture,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
thf(f24,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f69,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 )
<=> ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ),
inference(rectify,[],[f24]) ).
thf(f70,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) )
= ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f83,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ X0 @ X1 @ X2 @ X3 ) ) ),
inference(ennf_transformation,[],[f70]) ).
thf(f125,plain,
( ( ~ ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f83]) ).
thf(f221,plain,
( ( ~ ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) )
!= ( ~ ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f283,plain,
( ( $true
= ( ~ ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) ) )
| ( $true
= ( ~ ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) ) ) ),
inference(xor_proxy_clausification,[],[f221]) ).
thf(f284,plain,
( ( ( ~ ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) )
= $false )
| ( ( ~ ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f221]) ).
thf(f285,plain,
( ( $true
= ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) )
| ( $true
= ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) ) ),
inference(not_proxy_clausification,[],[f284]) ).
thf(f286,plain,
( $true
= ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 ) ),
inference(duplicate_literal_removal,[],[f285]) ).
thf(f287,plain,
( ( ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 )
= $false )
| ( ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 )
= $false ) ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f288,plain,
( ( c_2Ecardinal_2Ecardleq @ sK6 @ sK7 @ sK8 @ sK9 )
= $false ),
inference(duplicate_literal_removal,[],[f287]) ).
thf(f414,plain,
$true = $false,
inference(constrained_superposition,[],[f286,f288]) ).
thf(f415,plain,
$false,
inference(trivial_inequality_removal,[],[f414]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP010^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.28 % Computer : n003.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Sep 29 19:26:59 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.29/0.33 Running first-order model finding
% 0.29/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.29/0.39 % (2947276)Will run a generic schedule for satisfiability detection.
% 0.29/0.39 % (2947285)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=437356179:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.29/0.39 % (2947285)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.29/0.39 % (2947285) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2947276-2947285"...
% 0.29/0.39 % (2947282)% WARNING: option uhcvi not known.
% 0.29/0.39 % (2947285)...printing done.
% 0.29/0.39 % (2947285)Refutation found. Thanks to Tanya!
% 0.29/0.39 % SZS status Theorem for theBenchmark
% 0.29/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.39 % (2947285)------------------------------
% 0.29/0.39 % (2947285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.39 % (2947285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.39 % (2947285)CaDiCaL version: 2.1.3
% 0.29/0.39 % (2947285)Termination reason: Refutation
% 0.29/0.39 % (2947285)Time elapsed: 0.006 s
% 0.29/0.39 % (2947285)Peak memory usage: 12 MB
% 0.29/0.39 % (2947285)Instructions burned: 11 (million)
% 0.29/0.39 % (2947276)Success in time 0.043 s
% 0.29/0.39 % Vampire exiting
%------------------------------------------------------------------------------