%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM756^1 : 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 08:19:28 AM UTC 2026
% Result : Theorem 0.18s 0.28s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 278 ( 82 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 431 ( 76 ~; 29 |; 4 &; 288 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 ^; 72 !; 0 ?; 72 :)
% 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,
eq: frac > frac > $o ).
thf(func_def_4,type,
pf: frac > frac > frac ).
thf(func_def_6,type,
lessf: frac > frac > $o ).
thf(func_def_7,type,
moref: frac > frac > $o ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(f1,axiom,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(f3,axiom,
! [X0: frac,X1: frac] :
~ ( ( ( eq @ X0 @ X1 )
=> ~ ( moref @ X0 @ X1 ) )
=> ~ ~ ( ( ( moref @ X0 @ X1 )
=> ~ ( lessf @ X0 @ X1 ) )
=> ~ ( ( lessf @ X0 @ X1 )
=> ~ ( eq @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41b) ).
thf(f4,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X0 @ X1 )
=> ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62c) ).
thf(f5,axiom,
! [X0: frac,X1: frac] :
( ~ ( eq @ X0 @ X1 )
=> ( ~ ( moref @ X0 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41a) ).
thf(f6,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62a) ).
thf(f7,conjecture,
eq @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz63b) ).
thf(f8,negated_conjecture,
~ ( eq @ x @ y ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f13,plain,
! [X0: frac,X1: frac] :
~ ( ( ( eq @ X0 @ X1 )
=> ~ ( moref @ X0 @ X1 ) )
=> ~ ~ ( ( ( moref @ X0 @ X1 )
=> ~ ( lessf @ X0 @ X1 ) )
=> ~ ( ( lessf @ X0 @ X1 )
=> ~ ( eq @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
! [X0: frac,X1: frac] :
~ ( ( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( moref @ X0 @ X1 )
!= $true ) )
=> ~ ~ ( ( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( lessf @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( eq @ X0 @ X1 )
!= $true ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X0 @ X1 )
=> ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
! [X0: frac,X1: frac] :
( ~ ( eq @ X0 @ X1 )
=> ( ~ ( moref @ X0 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
=> ( ( ( moref @ X0 @ X1 )
!= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( eq @ x @ y ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
( ( eq @ x @ y )
!= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f24,plain,
! [X0: frac,X1: frac] :
~ ( ( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( moref @ X0 @ X1 )
!= $true ) )
=> ( ( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( lessf @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( eq @ X0 @ X1 )
!= $true ) ) ) ),
inference(flattening,[],[f14]) ).
thf(f25,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
=> ( ( ( moref @ X0 @ X1 )
!= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[],[f18]) ).
thf(f26,plain,
( ( eq @ x @ y )
!= $true ),
inference(flattening,[],[f22]) ).
thf(f28,plain,
! [X0: frac,X1: frac] :
( ( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) )
& ( ( ( lessf @ X0 @ X1 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) )
& ( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f29,plain,
! [X0: frac,X1: frac] :
( ( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) )
& ( ( ( lessf @ X0 @ X1 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) )
& ( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f28]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f31,plain,
! [X0: frac,X1: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
| ( ( moref @ X0 @ X1 )
= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f32,plain,
! [X0: frac,X1: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
| ( ( moref @ X0 @ X1 )
= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(flattening,[],[f31]) ).
thf(f33,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f34,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f36,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f38,plain,
! [X0: frac,X1: frac] :
( ( ( lessf @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f39,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
| ( ( lessf @ X0 @ X1 )
= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f41,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f42,plain,
( ( eq @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f26]) ).
thf(f80,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( lessf @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f38,f39]) ).
thf(f81,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( lessf @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f95,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( moref @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f36,f41]) ).
thf(f96,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( moref @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f103,plain,
( ( $true != $true )
| ( $true
!= ( lessf @ x @ y ) ) ),
inference(constrained_superposition,[],[f81,f34]) ).
thf(f104,plain,
( $true
!= ( lessf @ x @ y ) ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f107,plain,
( ( $true != $true )
| ( $true
!= ( moref @ x @ y ) ) ),
inference(constrained_superposition,[],[f96,f34]) ).
thf(f108,plain,
( $true
!= ( moref @ x @ y ) ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f120,plain,
( ( $true != $true )
| ( $true
= ( lessf @ x @ y ) )
| ( ( eq @ x @ y )
= $true ) ),
inference(constrained_superposition,[],[f108,f40]) ).
thf(f122,plain,
( ( $true
= ( lessf @ x @ y ) )
| ( ( eq @ x @ y )
= $true ) ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f124,plain,
( ( eq @ x @ y )
= $true ),
inference(forward_subsumption_resolution,[],[f122,f104]) ).
thf(f125,plain,
$false,
inference(forward_subsumption_resolution,[],[f124,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM756^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n010.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 12:52:47 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.18/0.28 % (2803330)Will run a generic schedule for satisfiability detection.
% 0.18/0.28 % (2803335)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2792996568_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.28 % Exception at run slice level
% 0.18/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.28 % (2803336)% WARNING: option uhcvi not known.
% 0.18/0.28 % (2803336)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1728192152:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.28 % (2803338)dis+10_1_sil=32000:sp=arity:random_seed=1321586643:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.28 % (2803337)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=908713492:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.28 % (2803339)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3342964446:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.28 % (2803336)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.28 % (2803339)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.28 % (2803336)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.28 % (2803343)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1500284696:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.28 % (2803340)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4119431306:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.28 % Exception at run slice level
% 0.18/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.28 % (2803339) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2803330-2803339"...
% 0.18/0.28 % (2803341)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=199727678:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.28 % (2803339)...printing done.
% 0.18/0.28 % (2803338) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2803330-2803338"...
% 0.18/0.28 % (2803339)Refutation found. Thanks to Tanya!
% 0.18/0.28 % SZS status Theorem for theBenchmark
% 0.18/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.28 % (2803339)------------------------------
% 0.18/0.28 % (2803339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28 % (2803339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28 % (2803339)CaDiCaL version: 2.1.3
% 0.18/0.28 % (2803339)Termination reason: Refutation
% 0.18/0.28 % (2803339)Time elapsed: 0.006 s
% 0.18/0.28 % (2803339)Peak memory usage: 12 MB
% 0.18/0.28 % (2803339)Instructions burned: 8 (million)
% 0.18/0.28 % (2803330)Success in time 0.05 s
% 0.18/0.28 % Vampire exiting
%------------------------------------------------------------------------------