%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM754^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:19:27 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 198 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 325 ( 41 ~; 27 |; 0 &; 242 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% 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,
z: frac ).
thf(func_def_3,type,
u: frac ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_6,type,
moref: frac > frac > $o ).
thf(func_def_7,type,
pf: frac > frac > frac ).
thf(f1,axiom,
eq @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(f2,axiom,
moref @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(f3,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).
thf(f4,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X0 @ X1 )
=> ( ( moref @ X2 @ X3 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62g) ).
thf(f5,axiom,
! [X0: frac,X1: frac] : ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz58) ).
thf(f6,conjecture,
moref @ ( pf @ z @ x ) @ ( pf @ u @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62h) ).
thf(f7,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
eq @ x @ y,
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ( eq @ x @ y )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
moref @ z @ u,
inference(rectify,[],[f2]) ).
thf(f11,plain,
( ( moref @ z @ u )
= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X0 @ X2 )
= $true )
=> ( ( ( eq @ X1 @ X3 )
= $true )
=> ( ( moref @ X2 @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X0 @ X1 )
=> ( ( moref @ X2 @ X3 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( ( moref @ X2 @ X3 )
= $true )
=> ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
! [X0: frac,X1: frac] : ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) )
= $true ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) )
!= $true ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) )
!= $true ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f21]) ).
thf(f23,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true )
| ( ( moref @ X2 @ X3 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f24,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true )
| ( ( moref @ X2 @ X3 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
( ( eq @ x @ y )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f26,plain,
( ( moref @ z @ u )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f27,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f28,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true )
| ( ( moref @ X2 @ X3 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f29,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f30,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) )
!= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f56,plain,
! [X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ X0 @ ( pf @ u @ y ) ) )
| ( $true
!= ( eq @ X1 @ ( pf @ z @ x ) ) )
| ( $true
!= ( moref @ X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f30,f27]) ).
thf(f57,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ ( pf @ u @ y ) ) )
| ( $true
!= ( eq @ X1 @ ( pf @ z @ x ) ) )
| ( $true
!= ( moref @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f71,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ X0 @ ( pf @ u @ y ) ) )
| ( $true
!= ( moref @ ( pf @ x @ z ) @ X0 ) ) ),
inference(constrained_superposition,[],[f57,f29]) ).
thf(f76,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ ( pf @ u @ y ) ) )
| ( $true
!= ( moref @ ( pf @ x @ z ) @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f132,plain,
( ( $true != $true )
| ( $true
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(constrained_superposition,[],[f76,f29]) ).
thf(f139,plain,
( $true
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f324,plain,
( ( $true != $true )
| ( ( moref @ z @ u )
!= $true )
| ( ( eq @ x @ y )
!= $true ) ),
inference(constrained_superposition,[],[f139,f28]) ).
thf(f334,plain,
( ( ( moref @ z @ u )
!= $true )
| ( ( eq @ x @ y )
!= $true ) ),
inference(trivial_inequality_removal,[],[f324]) ).
thf(f336,plain,
( ( eq @ x @ y )
!= $true ),
inference(forward_subsumption_resolution,[],[f334,f26]) ).
thf(f337,plain,
$false,
inference(forward_subsumption_resolution,[],[f336,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM754^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:51:59 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.28 % (1004527)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (1004532)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=962835333_2999 on theBenchmark for (2999ds/0Mi)
% 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 % (1004533)% WARNING: option uhcvi not known.
% 0.20/0.28 % (1004533)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3694808271:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (1004534)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2107319436:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (1004535)dis+10_1_sil=32000:sp=arity:random_seed=3887210325:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (1004536)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2136070482:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (1004533)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (1004538)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3140537605:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (1004533)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (1004537)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1589646525:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (1004536)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (1004540)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=788553755:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 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 % (1004548)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3319816092:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (1004536) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1004527-1004536"...
% 0.20/0.28 % (1004536)...printing done.
% 0.20/0.28 % (1004537) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1004527-1004537"...
% 0.20/0.28 % (1004536)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 % (1004536)------------------------------
% 0.20/0.28 % (1004536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1004536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1004536)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1004536)Termination reason: Refutation
% 0.20/0.28 % (1004536)Time elapsed: 0.018 s
% 0.20/0.28 % (1004536)Peak memory usage: 12 MB
% 0.20/0.28 % (1004536)Instructions burned: 33 (million)
% 0.20/0.28 % (1004527)Success in time 0.053 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------