%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO171^5 : 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 : n016.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 08:49:05 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 212 ( 41 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 278 ( 50 ~; 44 |; 20 &; 162 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
g: $i > $i > $o ).
thf(func_def_2,type,
f: $i > $i ).
thf(f1,conjecture,
~ ( ! [X0: $i,X1: $i] :
( ~ ( g @ X1 @ a )
| ~ ( g @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( g @ X1 @ ( f @ X1 ) )
| ~ ( g @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( g @ ( f @ X1 ) @ X1 )
| ~ ( g @ X0 @ X1 ) )
& ! [X0: $i] :
( ( g @ X0 @ ( f @ X0 ) )
| ( g @ X0 @ a ) )
& ! [X0: $i] :
( ( g @ ( f @ X0 ) @ X0 )
| ( g @ X0 @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSYN031_1) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X0: $i,X1: $i] :
( ~ ( g @ X1 @ a )
| ~ ( g @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( g @ X1 @ ( f @ X1 ) )
| ~ ( g @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( g @ ( f @ X1 ) @ X1 )
| ~ ( g @ X0 @ X1 ) )
& ! [X0: $i] :
( ( g @ X0 @ ( f @ X0 ) )
| ( g @ X0 @ a ) )
& ! [X0: $i] :
( ( g @ ( f @ X0 ) @ X0 )
| ( g @ X0 @ a ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( ~ ( g @ X1 @ a )
| ~ ( g @ X0 @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( g @ X3 @ ( f @ X3 ) )
| ~ ( g @ X2 @ X3 ) )
& ! [X4: $i,X5: $i] :
( ( g @ ( f @ X5 ) @ X5 )
| ~ ( g @ X4 @ X5 ) )
& ! [X6: $i] :
( ( g @ X6 @ ( f @ X6 ) )
| ( g @ X6 @ a ) )
& ! [X7: $i] :
( ( g @ ( f @ X7 ) @ X7 )
| ( g @ X7 @ a ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X1 @ a )
!= $true )
| ( ( g @ X0 @ X1 )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( g @ X3 @ ( f @ X3 ) )
= $true )
| ( ( g @ X2 @ X3 )
!= $true ) )
& ! [X4: $i,X5: $i] :
( ( ( g @ ( f @ X5 ) @ X5 )
= $true )
| ( ( g @ X4 @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( ( g @ X6 @ ( f @ X6 ) )
= $true )
| ( ( g @ X6 @ a )
= $true ) )
& ! [X7: $i] :
( ( ( g @ ( f @ X7 ) @ X7 )
= $true )
| ( ( g @ X7 @ a )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i,X1: $i] :
( ( ( g @ X1 @ a )
!= $true )
| ( ( g @ X0 @ X1 )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( g @ X3 @ ( f @ X3 ) )
= $true )
| ( ( g @ X2 @ X3 )
!= $true ) )
& ! [X4: $i,X5: $i] :
( ( ( g @ ( f @ X5 ) @ X5 )
= $true )
| ( ( g @ X4 @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( ( g @ X6 @ ( f @ X6 ) )
= $true )
| ( ( g @ X6 @ a )
= $true ) )
& ! [X7: $i] :
( ( ( g @ ( f @ X7 ) @ X7 )
= $true )
| ( ( g @ X7 @ a )
= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
! [X7: $i] :
( ( ( g @ ( f @ X7 ) @ X7 )
= $true )
| ( ( g @ X7 @ a )
= $true ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f7,plain,
! [X6: $i] :
( ( ( g @ X6 @ ( f @ X6 ) )
= $true )
| ( ( g @ X6 @ a )
= $true ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( g @ X1 @ a )
!= $true )
| ( ( g @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f13,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( g @ X0 @ ( f @ a ) ) )
| ( $true
= ( g @ a @ a ) ) ),
inference(constrained_superposition,[],[f10,f6]) ).
thf(f14,plain,
! [X0: $i] :
( ( $true
!= ( g @ X0 @ ( f @ a ) ) )
| ( $true
= ( g @ a @ a ) ) ),
inference(trivial_inequality_removal,[],[f13]) ).
thf(f16,definition,
( spl0_1
<=> ( $true
= ( g @ a @ a ) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f18,plain,
( ( $true
= ( g @ a @ a ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f20,definition,
( spl0_2
<=> ! [X0: $i] :
( $true
!= ( g @ X0 @ ( f @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f21,plain,
( ! [X0: $i] :
( $true
!= ( g @ X0 @ ( f @ a ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f14,f20,f16]) ).
thf(f26,plain,
( ( $true != $true )
| ( $true
= ( g @ a @ a ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f21,f7]) ).
thf(f27,plain,
( ( $true
= ( g @ a @ a ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f29,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f27,f20,f16]) ).
thf(f51,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( g @ X0 @ a )
!= $true ) )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f10,f18]) ).
thf(f52,plain,
( ! [X0: $i] :
( ( g @ X0 @ a )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f59,plain,
( $false
| ~ spl0_1 ),
inference(backward_subsumption_resolution,[],[f18,f52]) ).
thf(f62,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f62]) ).
cnf(s5,plain,
~ spl0_2,
inference(rat,[],[s2,s4]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s4]) ).
thf(f63,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO171^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n016.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 16:41:35 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.20/0.27 % (585455)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (585462)% WARNING: option uhcvi not known.
% 0.20/0.27 % (585462)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2875156550:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (585462)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (585462)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.27 % (585462) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-585455-585462"...
% 0.20/0.27 % (585462)...printing done.
% 0.20/0.27 % (585462)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (585462)------------------------------
% 0.20/0.27 % (585462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (585462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (585462)CaDiCaL version: 2.1.3
% 0.20/0.27 % (585462)Termination reason: Refutation
% 0.20/0.27 % (585462)Time elapsed: 0.003 s
% 0.20/0.27 % (585462)Peak memory usage: 13 MB
% 0.20/0.27 % (585462)Instructions burned: 5 (million)
% 0.20/0.27 % (585455)Success in time 0.031 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------