%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM755^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:18:46 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 296 ( 88 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 452 ( 80 ~; 30 |; 6 &; 302 @)
% ( 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 : 65 ( 0 ^; 65 !; 0 ?; 65 :)
% 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,
moref: frac > frac > $o ).
thf(func_def_4,type,
pf: frac > frac > frac ).
thf(func_def_6,type,
eq: frac > frac > $o ).
thf(func_def_7,type,
lessf: frac > frac > $o ).
thf(f1,axiom,
moref @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
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/sandbox/benchmark/theBenchmark.p',satz41b) ).
thf(f4,axiom,
! [X2: frac,X1: frac,X0: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62b) ).
thf(f5,axiom,
! [X0: frac,X2: frac,X1: frac] :
( ( lessf @ X0 @ X1 )
=> ( lessf @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62c) ).
thf(f6,axiom,
! [X1: frac,X0: frac] :
( ~ ( eq @ X0 @ X1 )
=> ( ~ ( moref @ X0 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41a) ).
thf(f7,conjecture,
moref @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz63a) ).
thf(f8,negated_conjecture,
~ ( moref @ x @ y ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
~ ( moref @ x @ y ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( moref @ x @ y )
!= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f13,plain,
! [X0: frac,X1: frac] :
( ~ ( eq @ X1 @ X0 )
=> ( ~ ( moref @ X1 @ X0 )
=> ( lessf @ X1 @ X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
=> ( ( ( moref @ X1 @ X0 )
!= $true )
=> ( ( lessf @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
moref @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(rectify,[],[f1]) ).
thf(f16,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X2 @ X1 )
=> ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f18,plain,
! [X2: frac,X1: frac,X0: frac] :
( ( ( eq @ X2 @ X1 )
= $true )
=> ( $true
= ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ) ),
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,[],[f5]) ).
thf(f20,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( lessf @ X0 @ X2 )
= $true )
=> ( $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] :
~ ( ( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( moref @ X1 @ X0 )
!= $true ) )
=> ~ ~ ( ( ( ( moref @ X1 @ X0 )
= $true )
=> ( ( lessf @ X1 @ X0 )
!= $true ) )
=> ~ ( ( ( lessf @ X1 @ X0 )
= $true )
=> ( ( eq @ X1 @ X0 )
!= $true ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ( moref @ x @ y )
!= $true ),
inference(flattening,[],[f10]) ).
thf(f25,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
=> ( ( ( moref @ X1 @ X0 )
!= $true )
=> ( ( lessf @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[],[f14]) ).
thf(f26,plain,
! [X1: frac,X0: frac] :
~ ( ( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( moref @ X1 @ X0 )
!= $true ) )
=> ( ( ( ( moref @ X1 @ X0 )
= $true )
=> ( ( lessf @ X1 @ X0 )
!= $true ) )
=> ~ ( ( ( lessf @ X1 @ X0 )
= $true )
=> ( ( eq @ X1 @ X0 )
!= $true ) ) ) ),
inference(flattening,[],[f22]) ).
thf(f27,plain,
! [X1: frac,X0: frac] :
( ( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( lessf @ X1 @ X0 )
!= $true ) )
& ( ( ( moref @ X1 @ X0 )
!= $true )
| ( ( lessf @ X1 @ X0 )
!= $true ) )
& ( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( moref @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f28,plain,
! [X1: frac,X0: frac] :
( ( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( lessf @ X1 @ X0 )
!= $true ) )
& ( ( ( moref @ X1 @ X0 )
!= $true )
| ( ( lessf @ X1 @ X0 )
!= $true ) )
& ( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( moref @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f27]) ).
thf(f29,plain,
! [X0: frac,X1: frac] :
( ( ( lessf @ X1 @ X0 )
= $true )
| ( ( moref @ X1 @ X0 )
= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f30,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( moref @ X1 @ X0 )
= $true )
| ( ( lessf @ X1 @ X0 )
= $true ) ),
inference(flattening,[],[f29]) ).
thf(f31,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( $true
= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( ( lessf @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f33,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X2 @ X1 )
!= $true )
| ( $true
= ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) )
= $true )
| ( $true
!= ( lessf @ X1 @ X2 ) ) ),
inference(rectify,[],[f31]) ).
thf(f35,plain,
! [X0: frac,X1: frac] :
( ( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) )
& ( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) )
& ( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ) ),
inference(rectify,[],[f28]) ).
thf(f37,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( lessf @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) )
= $true )
| ( $true
!= ( lessf @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f38,plain,
( ( moref @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f39,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) )
| ( ( eq @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f40,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f41,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f42,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f44,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
| ( ( lessf @ X1 @ X0 )
= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f47,plain,
( ( $true != $true )
| ( $true
!= ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ),
inference(superposition,[],[f42,f40]) ).
thf(f48,plain,
( ( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f41,f40]) ).
thf(f49,plain,
( $true
!= ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f50,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= $true ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f51,plain,
( ( $true
= ( eq @ x @ y ) )
| ( $true != $true )
| ( $true
= ( lessf @ x @ y ) ) ),
inference(superposition,[],[f38,f44]) ).
thf(f54,plain,
( ( $true
= ( lessf @ x @ y ) )
| ( $true
= ( eq @ x @ y ) ) ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f56,plain,
( ( $true
!= ( lessf @ x @ y ) )
| ( $true != $true ) ),
inference(superposition,[],[f49,f37]) ).
thf(f58,plain,
( $true
!= ( lessf @ x @ y ) ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f60,plain,
( ( $true
!= ( eq @ x @ y ) )
| ( $true != $true ) ),
inference(superposition,[],[f50,f39]) ).
thf(f61,plain,
( $true
!= ( eq @ x @ y ) ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f62,plain,
( ( $true
= ( eq @ x @ y ) )
| ( $true != $true ) ),
inference(superposition,[],[f58,f54]) ).
thf(f63,plain,
( $true
= ( eq @ x @ y ) ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f64,plain,
$false,
inference(forward_subsumption_resolution,[],[f61,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM755^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:51:10 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (666395)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (666404)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=8131722:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (666404) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-666395-666404"...
% 0.20/0.28 % (666404)...printing done.
% 0.20/0.28 % (666404)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 % (666404)------------------------------
% 0.20/0.28 % (666404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (666404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (666404)CaDiCaL version: 2.1.3
% 0.20/0.28 % (666404)Termination reason: Refutation
% 0.20/0.28 % (666404)Time elapsed: 0.002 s
% 0.20/0.28 % (666404)Peak memory usage: 12 MB
% 0.20/0.28 % (666404)Instructions burned: 6 (million)
% 0.20/0.28 % (666395)Success in time 0.032 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------