%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM756^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:18:47 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 293 ( 87 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 447 ( 75 ~; 30 |; 4 &; 304 @)
% ( 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 : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% 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(f1,axiom,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(f3,axiom,
! [X1: frac,X0: frac] :
~ ( ( ( eq @ X0 @ X1 )
=> ~ ( moref @ X0 @ X1 ) )
=> ~ ~ ( ( ( moref @ X0 @ X1 )
=> ~ ( lessf @ X0 @ X1 ) )
=> ~ ( ( lessf @ X0 @ X1 )
=> ~ ( eq @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41b) ).
thf(f4,axiom,
! [X0: frac,X2: frac,X1: frac] :
( ( lessf @ X0 @ X1 )
=> ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62c) ).
thf(f5,axiom,
! [X0: frac,X1: frac] :
( ~ ( eq @ X0 @ X1 )
=> ( ~ ( moref @ X0 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41a) ).
thf(f6,axiom,
! [X2: frac,X1: frac,X0: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62a) ).
thf(f7,conjecture,
eq @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63b) ).
thf(f8,negated_conjecture,
~ ( eq @ x @ y ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f11,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X2 @ X1 )
=> ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
! [X2: frac,X1: frac,X0: frac] :
( ( $true
= ( moref @ X2 @ X1 ) )
=> ( $true
= ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ( eq @ x @ y ),
inference(rectify,[],[f8]) ).
thf(f14,plain,
( ( eq @ x @ y )
!= $true ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: frac,X1: frac] :
( ~ ( eq @ X0 @ X1 )
=> ( ~ ( moref @ X0 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f16,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
=> ( ( ( moref @ X0 @ X1 )
!= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(rectify,[],[f1]) ).
thf(f18,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X0 @ X2 )
=> ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f20,plain,
! [X1: frac,X2: frac,X0: frac] :
( ( $true
= ( lessf @ X0 @ X2 ) )
=> ( $true
= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
~ ( ( ( eq @ X1 @ X0 )
=> ~ ( moref @ X1 @ X0 ) )
=> ~ ~ ( ( ( moref @ X1 @ X0 )
=> ~ ( lessf @ X1 @ X0 ) )
=> ~ ( ( lessf @ X1 @ X0 )
=> ~ ( eq @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f22,plain,
! [X0: frac,X1: frac] :
~ ( ( ( $true
= ( eq @ X1 @ X0 ) )
=> ( ( moref @ X1 @ X0 )
!= $true ) )
=> ~ ~ ( ( ( ( moref @ X1 @ X0 )
= $true )
=> ( $true
!= ( lessf @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( lessf @ X1 @ X0 ) )
=> ( $true
!= ( eq @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f24,plain,
( ( eq @ x @ y )
!= $true ),
inference(flattening,[],[f14]) ).
thf(f25,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
=> ( ( ( moref @ X0 @ X1 )
!= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[],[f16]) ).
thf(f26,plain,
! [X0: frac,X1: frac] :
~ ( ( ( $true
= ( eq @ X1 @ X0 ) )
=> ( ( moref @ X1 @ X0 )
!= $true ) )
=> ( ( ( ( moref @ X1 @ X0 )
= $true )
=> ( $true
!= ( lessf @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( lessf @ X1 @ X0 ) )
=> ( $true
!= ( eq @ X1 @ X0 ) ) ) ) ),
inference(flattening,[],[f22]) ).
thf(f27,plain,
! [X1: frac,X2: frac,X0: frac] :
( ( $true
= ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) )
| ( $true
!= ( moref @ X2 @ X1 ) ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f28,plain,
! [X1: frac,X0: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
| ( ( moref @ X0 @ X1 )
= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f29,plain,
! [X1: frac,X0: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
| ( ( lessf @ X0 @ X1 )
= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(flattening,[],[f28]) ).
thf(f30,plain,
! [X0: frac,X1: frac] :
( ( ( $true
!= ( eq @ X1 @ X0 ) )
| ( $true
!= ( lessf @ X1 @ X0 ) ) )
& ( ( $true
!= ( lessf @ X1 @ X0 ) )
| ( ( moref @ X1 @ X0 )
!= $true ) )
& ( ( ( moref @ X1 @ X0 )
!= $true )
| ( $true
!= ( eq @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f31,plain,
! [X0: frac,X1: frac] :
( ( ( $true
!= ( lessf @ X1 @ X0 ) )
| ( ( moref @ X1 @ X0 )
!= $true ) )
& ( ( $true
!= ( eq @ X1 @ X0 ) )
| ( $true
!= ( lessf @ X1 @ X0 ) ) )
& ( ( ( moref @ X1 @ X0 )
!= $true )
| ( $true
!= ( eq @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( $true
= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( lessf @ X0 @ X2 ) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X2 ) ) )
| ( ( moref @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f27]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f32]) ).
thf(f36,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
| ( $true
= ( lessf @ X1 @ X0 ) )
| ( $true
= ( eq @ X1 @ X0 ) ) ),
inference(rectify,[],[f29]) ).
thf(f37,plain,
( ( eq @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f24]) ).
thf(f39,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X2 ) ) )
| ( ( moref @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X1 @ X0 ) )
| ( ( moref @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f41,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X1 @ X0 ) )
| ( $true
!= ( lessf @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f43,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f44,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f45,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( eq @ X1 @ X0 ) )
| ( $true
= ( lessf @ X1 @ X0 ) )
| ( ( moref @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f48,plain,
( ( ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f41,f43]) ).
thf(f49,plain,
( ( $true != $true )
| ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= $true ) ),
inference(superposition,[],[f40,f43]) ).
thf(f50,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= $true ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f51,plain,
( ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= $true ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f52,plain,
( ( $true != $true )
| ( ( moref @ x @ y )
= $true )
| ( $true
= ( lessf @ x @ y ) ) ),
inference(superposition,[],[f37,f45]) ).
thf(f55,plain,
( ( ( moref @ x @ y )
= $true )
| ( $true
= ( lessf @ x @ y ) ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f57,plain,
( ( $true != $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(superposition,[],[f50,f39]) ).
thf(f59,plain,
( ( moref @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f61,plain,
( ( $true
!= ( lessf @ x @ y ) )
| ( $true != $true ) ),
inference(superposition,[],[f51,f44]) ).
thf(f62,plain,
( $true
!= ( lessf @ x @ y ) ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f63,plain,
( ( $true != $true )
| ( $true
= ( lessf @ x @ y ) ) ),
inference(superposition,[],[f59,f55]) ).
thf(f64,plain,
( $true
= ( lessf @ x @ y ) ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f65,plain,
$false,
inference(forward_subsumption_resolution,[],[f62,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM756^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n015.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 12:55:47 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.28 % (3473364)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (3473371)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2412211450:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (3473371)Instruction limit reached!
% 0.19/0.28 % (3473371)------------------------------
% 0.19/0.28 % (3473371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3473371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3473371)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3473371)Termination reason: Instruction limit
% 0.19/0.28 % (3473371)Time elapsed: 0.002 s
% 0.19/0.28 % (3473371)Peak memory usage: 12 MB
% 0.19/0.28 % (3473371)Instructions burned: 5 (million)
% 0.19/0.28 % (3473375)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (3473375)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.19/0.28 % (3473369)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1970871344:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (3473370)lrs+10_16_si=on:nwc=1.5:random_seed=2234999587:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (3473373)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1376329572:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.28 % (3473372)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2959761186:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.28 % (3473374)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=94116613:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.28 % (3473375)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1983167277:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (3473373) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3473364-3473373"...
% 0.19/0.28 % (3473369) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3473364-3473369"...
% 0.19/0.28 % (3473370) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3473364-3473370"...
% 0.19/0.28 % (3473372) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3473364-3473372"...
% 0.19/0.28 % (3473377)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2504531471:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.28 % (3473373)...printing done.
% 0.19/0.28 % (3473369)...printing done.
% 0.19/0.28 % (3473370)...printing done.
% 0.19/0.28 % (3473375) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3473364-3473375"...
% 0.19/0.28 % (3473374) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3473364-3473374"...
% 0.19/0.28 % (3473377)Instruction limit reached!
% 0.19/0.28 % (3473377)------------------------------
% 0.19/0.28 % (3473377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3473377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3473377)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3473377)Termination reason: Instruction limit
% 0.19/0.28 % (3473377)Termination phase: Saturation
% 0.19/0.28 % (3473377)Time elapsed: 0.001 s
% 0.19/0.28 % (3473377)Peak memory usage: 12 MB
% 0.19/0.28 % (3473377)Instructions burned: 3 (million)
% 0.19/0.28 % (3473373)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (3473373)------------------------------
% 0.19/0.29 % (3473373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (3473373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (3473373)CaDiCaL version: 2.1.3
% 0.19/0.29 % (3473373)Termination reason: Refutation
% 0.19/0.29 % (3473373)Time elapsed: 0.004 s
% 0.19/0.29 % (3473373)Peak memory usage: 12 MB
% 0.19/0.29 % (3473373)Instructions burned: 6 (million)
% 0.19/0.29 % (3473364)Success in time 0.047 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------