%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM770^1 : 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 : n010.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 08:19:30 AM UTC 2026
% Result : Theorem 0.11s 0.23s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 37 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 225 ( 19 ~; 13 |; 0 &; 184 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% 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,
v: frac ).
thf(func_def_3,type,
moref: frac > frac > $o ).
thf(func_def_5,type,
eq: frac > frac > $o ).
thf(func_def_6,type,
pf: frac > frac > frac ).
thf(func_def_7,type,
mf: frac > frac > frac ).
thf(f1,axiom,
moref @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
eq @ ( pf @ y @ v ) @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(f3,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ ( pf @ X1 @ X2 ) @ X0 )
=> ( ( eq @ ( pf @ X1 @ X3 ) @ X0 )
=> ( eq @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz67b) ).
thf(f4,axiom,
! [X0: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz67c) ).
thf(f5,conjecture,
eq @ v @ ( mf @ x @ y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz67e) ).
thf(f6,negated_conjecture,
~ ( eq @ v @ ( mf @ x @ y ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
moref @ x @ y,
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ( moref @ x @ y )
= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
eq @ ( pf @ y @ v ) @ x,
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ( eq @ ( pf @ y @ v ) @ x )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ ( pf @ X1 @ X2 ) @ X0 )
=> ( ( eq @ ( pf @ X1 @ X3 ) @ X0 )
=> ( eq @ X2 @ X3 ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ ( pf @ X1 @ X2 ) @ X0 )
= $true )
=> ( ( ( eq @ ( pf @ X1 @ X3 ) @ X0 )
= $true )
=> ( ( eq @ X2 @ X3 )
= $true ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 )
= $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( eq @ v @ ( mf @ x @ y ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( ( eq @ v @ ( mf @ x @ y ) )
!= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( eq @ v @ ( mf @ x @ y ) )
!= $true ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ X2 @ X3 )
= $true )
| ( ( eq @ ( pf @ X1 @ X3 ) @ X0 )
!= $true )
| ( ( eq @ ( pf @ X1 @ X2 ) @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ X2 @ X3 )
= $true )
| ( ( eq @ ( pf @ X1 @ X3 ) @ X0 )
!= $true )
| ( ( eq @ ( pf @ X1 @ X2 ) @ X0 )
!= $true ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f21,plain,
( ( moref @ x @ y )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f22,plain,
( ( eq @ ( pf @ y @ v ) @ x )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X1 @ X3 ) @ X0 )
!= $true )
| ( ( eq @ X2 @ X3 )
= $true )
| ( ( eq @ ( pf @ X1 @ X2 ) @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f24,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ ( pf @ X1 @ ( mf @ X0 @ X1 ) ) @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f25,plain,
( ( eq @ v @ ( mf @ x @ y ) )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f41,plain,
( ( $true != $true )
| ( $true
= ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x ) ) ),
inference(constrained_superposition,[],[f24,f21]) ).
thf(f42,plain,
( $true
= ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x ) ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f46,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
= ( eq @ X0 @ ( mf @ x @ y ) ) )
| ( $true
!= ( eq @ ( pf @ y @ X0 ) @ x ) ) ),
inference(constrained_superposition,[],[f23,f42]) ).
thf(f49,plain,
! [X0: frac] :
( ( $true
!= ( eq @ ( pf @ y @ X0 ) @ x ) )
| ( $true
= ( eq @ X0 @ ( mf @ x @ y ) ) ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f90,plain,
( ( $true != $true )
| ( ( eq @ v @ ( mf @ x @ y ) )
= $true ) ),
inference(constrained_superposition,[],[f49,f22]) ).
thf(f96,plain,
( ( eq @ v @ ( mf @ x @ y ) )
= $true ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f106,plain,
$true != $true,
inference(constrained_superposition,[],[f25,f96]) ).
thf(f107,plain,
$false,
inference(trivial_inequality_removal,[],[f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM770^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.16 % Computer : n010.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 12:55:18 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 Running first-order model finding
% 0.11/0.19 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
% 0.11/0.23 % (2806316)Will run a generic schedule for satisfiability detection.
% 0.11/0.23 % (2806327)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4097553992:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.23 % (2806327) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2806316-2806327"...
% 0.11/0.23 % (2806322)% WARNING: option uhcvi not known.
% 0.11/0.23 % (2806327)...printing done.
% 0.11/0.23 % (2806327)Refutation found. Thanks to Tanya!
% 0.11/0.23 % SZS status Theorem for theBenchmark
% 0.11/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.23 % (2806327)------------------------------
% 0.11/0.23 % (2806327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.23 % (2806327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.23 % (2806327)CaDiCaL version: 2.1.3
% 0.11/0.23 % (2806327)Termination reason: Refutation
% 0.11/0.23 % (2806327)Time elapsed: 0.003 s
% 0.11/0.23 % (2806327)Peak memory usage: 12 MB
% 0.11/0.23 % (2806327)Instructions burned: 7 (million)
% 0.11/0.23 % (2806316)Success in time 0.026 s
% 0.11/0.23 % Vampire exiting
%------------------------------------------------------------------------------