%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN058^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:41:50 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 13 unt; 0 typ; 6 def)
% Number of atoms : 369 ( 87 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 314 ( 67 ~; 51 |; 44 &; 122 @)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 48 !; 17 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: $i > $o ).
thf(func_def_1,type,
cF: $i > $o ).
thf(func_def_2,type,
cP: $i > $o ).
thf(func_def_3,type,
cS: $i > $o ).
thf(func_def_4,type,
cQ: $i > $o ).
thf(func_def_5,type,
cR: $i > $o ).
thf(f1,conjecture,
( ( ( ? [X0: $i] : ( cS @ X0 )
=> ! [X0: $i] :
( ( cF @ X0 )
=> ( cG @ X0 ) ) )
& ( ! [X0: $i] :
( ( cR @ X0 )
| ( cQ @ X0 ) )
=> ? [X0: $i] :
( ( cS @ X0 )
& ( cQ @ X0 ) ) )
& ! [X0: $i] :
( ( cP @ X0 )
=> ! [X1: $i] : ( cQ @ X1 ) ) )
=> ! [X0: $i] :
( ( ( cF @ X0 )
& ( cP @ X0 ) )
=> ( cG @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL28) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X0: $i] : ( cS @ X0 )
=> ! [X0: $i] :
( ( cF @ X0 )
=> ( cG @ X0 ) ) )
& ( ! [X0: $i] :
( ( cR @ X0 )
| ( cQ @ X0 ) )
=> ? [X0: $i] :
( ( cS @ X0 )
& ( cQ @ X0 ) ) )
& ! [X0: $i] :
( ( cP @ X0 )
=> ! [X1: $i] : ( cQ @ X1 ) ) )
=> ! [X0: $i] :
( ( ( cF @ X0 )
& ( cP @ X0 ) )
=> ( cG @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ? [X0: $i] : ( cS @ X0 )
=> ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) ) )
& ( ! [X2: $i] :
( ( cR @ X2 )
| ( cQ @ X2 ) )
=> ? [X3: $i] :
( ( cS @ X3 )
& ( cQ @ X3 ) ) )
& ! [X4: $i] :
( ( cP @ X4 )
=> ! [X5: $i] : ( cQ @ X5 ) ) )
=> ! [X6: $i] :
( ( ( cF @ X6 )
& ( cP @ X6 ) )
=> ( cG @ X6 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] :
( ( cS @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( cF @ X1 )
= $true )
=> ( ( cG @ X1 )
= $true ) ) )
& ( ! [X2: $i] :
( ( ( cR @ X2 )
= $true )
| ( ( cQ @ X2 )
= $true ) )
=> ? [X3: $i] :
( ( ( cS @ X3 )
= $true )
& ( ( cQ @ X3 )
= $true ) ) )
& ! [X4: $i] :
( ( ( cP @ X4 )
= $true )
=> ! [X5: $i] :
( ( cQ @ X5 )
= $true ) ) )
=> ! [X6: $i] :
( ( ( ( cF @ X6 )
= $true )
& ( ( cP @ X6 )
= $true ) )
=> ( ( cG @ X6 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X6: $i] :
( ( ( cG @ X6 )
!= $true )
& ( ( cF @ X6 )
= $true )
& ( ( cP @ X6 )
= $true ) )
& ( ! [X1: $i] :
( ( ( cG @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true ) )
| ! [X0: $i] :
( ( cS @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( ( cS @ X3 )
= $true )
& ( ( cQ @ X3 )
= $true ) )
| ? [X2: $i] :
( ( ( cR @ X2 )
!= $true )
& ( ( cQ @ X2 )
!= $true ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( cQ @ X5 )
= $true )
| ( ( cP @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X6: $i] :
( ( ( cG @ X6 )
!= $true )
& ( ( cF @ X6 )
= $true )
& ( ( cP @ X6 )
= $true ) )
& ( ! [X1: $i] :
( ( ( cG @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true ) )
| ! [X0: $i] :
( ( cS @ X0 )
!= $true ) )
& ( ? [X3: $i] :
( ( ( cS @ X3 )
= $true )
& ( ( cQ @ X3 )
= $true ) )
| ? [X2: $i] :
( ( ( cR @ X2 )
!= $true )
& ( ( cQ @ X2 )
!= $true ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( cQ @ X5 )
= $true )
| ( ( cP @ X4 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i] :
( ( ( cG @ X0 )
!= $true )
& ( ( cF @ X0 )
= $true )
& ( ( cP @ X0 )
= $true ) )
& ( ! [X1: $i] :
( ( ( cG @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true ) )
| ! [X2: $i] :
( $true
!= ( cS @ X2 ) ) )
& ( ? [X3: $i] :
( ( ( cS @ X3 )
= $true )
& ( ( cQ @ X3 )
= $true ) )
| ? [X4: $i] :
( ( $true
!= ( cR @ X4 ) )
& ( $true
!= ( cQ @ X4 ) ) ) )
& ! [X5: $i] :
( ! [X6: $i] :
( $true
= ( cQ @ X6 ) )
| ( $true
!= ( cP @ X5 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( cG @ sK0 ) )
& ( $true
= ( cF @ sK0 ) )
& ( $true
= ( cP @ sK0 ) )
& ( ! [X1: $i] :
( ( ( cG @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true ) )
| ! [X2: $i] :
( $true
!= ( cS @ X2 ) ) )
& ( ( ( $true
= ( cS @ sK1 ) )
& ( $true
= ( cQ @ sK1 ) ) )
| ( ( $true
!= ( cR @ sK2 ) )
& ( $true
!= ( cQ @ sK2 ) ) ) )
& ! [X5: $i] :
( ! [X6: $i] :
( $true
= ( cQ @ X6 ) )
| ( $true
!= ( cP @ X5 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X4,sK2)],[f7]) ).
thf(f9,plain,
! [X6: $i,X5: $i] :
( ( $true
= ( cQ @ X6 ) )
| ( $true
!= ( cP @ X5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( cS @ sK1 ) )
| ( $true
!= ( cQ @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X2: $i,X1: $i] :
( ( ( cG @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true )
| ( $true
!= ( cS @ X2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( $true
= ( cP @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( $true
= ( cF @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( $true
!= ( cG @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,definition,
( spl3_1
<=> ! [X5: $i] :
( $true
!= ( cP @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f22,plain,
( ! [X5: $i] :
( $true
!= ( cP @ X5 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,definition,
( spl3_2
<=> ! [X6: $i] :
( $true
= ( cQ @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f25,plain,
( ! [X6: $i] :
( $true
= ( cQ @ X6 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f26,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f9,f24,f21]) ).
thf(f28,definition,
( spl3_3
<=> ( $true
= ( cQ @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f30,plain,
( ( $true
!= ( cQ @ sK2 ) )
| spl3_3 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f42,definition,
( spl3_6
<=> ( $true
= ( cS @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f44,plain,
( ( $true
= ( cS @ sK1 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f45,plain,
( ~ spl3_3
| spl3_6 ),
inference(avatar_split_clause,[],[f12,f42,f28]) ).
thf(f48,definition,
( spl3_7
<=> ! [X2: $i] :
( $true
!= ( cS @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
thf(f49,plain,
( ! [X2: $i] :
( $true
!= ( cS @ X2 ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,definition,
( spl3_8
<=> ! [X1: $i] :
( ( ( cG @ X1 )
= $true )
| ( ( cF @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
thf(f52,plain,
( ! [X1: $i] :
( ( ( cF @ X1 )
!= $true )
| ( ( cG @ X1 )
= $true ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f53,plain,
( spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f14,f51,f48]) ).
thf(f54,plain,
( $false
| ~ spl3_2
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f30,f25]) ).
thf(f55,plain,
( ~ spl3_2
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f54]) ).
thf(f56,plain,
( $false
| ~ spl3_1 ),
inference(backward_subsumption_resolution,[],[f15,f22]) ).
thf(f57,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f56]) ).
thf(f58,plain,
( $false
| ~ spl3_6
| ~ spl3_7 ),
inference(backward_subsumption_resolution,[],[f44,f49]) ).
thf(f59,plain,
( ~ spl3_6
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f58]) ).
thf(f60,plain,
( ( $true != $true )
| ( $true
= ( cG @ sK0 ) )
| ~ spl3_8 ),
inference(constrained_superposition,[],[f52,f16]) ).
thf(f61,plain,
( ( $true
= ( cG @ sK0 ) )
| ~ spl3_8 ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f62,plain,
( $false
| ~ spl3_8 ),
inference(forward_subsumption_resolution,[],[f61,f17]) ).
thf(f63,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[],[f62]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s4,plain,
( ~ spl3_3
| spl3_6 ),
inference(sat_conversion,[],[f45]) ).
cnf(s6,plain,
( spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f53]) ).
cnf(s7,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f55]) ).
cnf(s8,plain,
~ spl3_1,
inference(sat_conversion,[],[f57]) ).
cnf(s9,plain,
( ~ spl3_6
| ~ spl3_7 ),
inference(sat_conversion,[],[f59]) ).
cnf(s10,plain,
~ spl3_8,
inference(sat_conversion,[],[f63]) ).
cnf(s11,plain,
spl3_7,
inference(rat,[],[s6,s10]) ).
cnf(s12,plain,
~ spl3_6,
inference(rat,[],[s9,s11]) ).
cnf(s14,plain,
~ spl3_3,
inference(rat,[],[s4,s12]) ).
cnf(s15,plain,
~ spl3_2,
inference(rat,[],[s7,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s15,s8]) ).
thf(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN058^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.16 % Computer : n014.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 16:14:30 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 Running first-order model finding
% 0.10/0.18 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
% 0.10/0.23 % (2862154)Will run a generic schedule for satisfiability detection.
% 0.10/0.23 % (2862160)% WARNING: option uhcvi not known.
% 0.10/0.23 % (2862160)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1143701643:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.23 % (2862160)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.23 % (2862160)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.23 % (2862160) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2862154-2862160"...
% 0.10/0.23 % (2862160)...printing done.
% 0.10/0.23 % (2862160)Refutation found. Thanks to Tanya!
% 0.10/0.23 % SZS status Theorem for theBenchmark
% 0.10/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.23 % (2862160)------------------------------
% 0.10/0.23 % (2862160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.23 % (2862160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.23 % (2862160)CaDiCaL version: 2.1.3
% 0.10/0.23 % (2862160)Termination reason: Refutation
% 0.10/0.23 % (2862160)Time elapsed: 0.002 s
% 0.10/0.23 % (2862160)Peak memory usage: 12 MB
% 0.10/0.23 % (2862160)Instructions burned: 4 (million)
% 0.10/0.23 % (2862154)Success in time 0.036 s
% 0.10/0.23 % Vampire exiting
%------------------------------------------------------------------------------