%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM765_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 : Tue Sep 29 12:25:39 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 167 ( 82 ~; 64 |; 5 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
frac: $tType ).
tff(func_def_0,type,
x: frac ).
tff(func_def_1,type,
y: frac ).
tff(func_def_2,type,
z: frac ).
tff(func_def_3,type,
u: frac ).
tff(func_def_4,type,
pf: ( frac * frac ) > frac ).
tff(pred_def_1,type,
moref: ( frac * frac ) > $o ).
tff(pred_def_2,type,
eq: ( frac * frac ) > $o ).
tff(f1,axiom,
( ~ moref(x,y)
=> eq(x,y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
tff(f2,axiom,
( ~ moref(z,u)
=> eq(z,u) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
tff(f4,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( eq(X0,X1)
=> ( eq(X2,X3)
=> eq(pf(X0,X2),pf(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56) ).
tff(f5,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(X0,X1)
=> ( ( ~ moref(X2,X3)
=> eq(X2,X3) )
=> moref(pf(X0,X2),pf(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz65b) ).
tff(f6,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ~ moref(X0,X1)
=> eq(X0,X1) )
=> ( moref(X2,X3)
=> moref(pf(X0,X2),pf(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz65a) ).
tff(f7,conjecture,
( ~ moref(pf(x,z),pf(y,u))
=> eq(pf(x,z),pf(y,u)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz66) ).
tff(f8,negated_conjecture,
~ ( ~ moref(pf(x,z),pf(y,u))
=> eq(pf(x,z),pf(y,u)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f12,plain,
( eq(x,y)
| moref(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f13,plain,
( eq(z,u)
| moref(z,u) ),
inference(ennf_transformation,[],[f2]) ).
tff(f15,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( eq(pf(X0,X2),pf(X1,X3))
| ~ eq(X2,X3)
| ~ eq(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f16,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( eq(pf(X0,X2),pf(X1,X3))
| ~ eq(X2,X3)
| ~ eq(X0,X1) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ( ~ eq(X2,X3)
& ~ moref(X2,X3) )
| ~ moref(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f18,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ( ~ eq(X2,X3)
& ~ moref(X2,X3) )
| ~ moref(X0,X1) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X2,X3)
| ( ~ eq(X0,X1)
& ~ moref(X0,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
tff(f20,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X2,X3)
| ( ~ eq(X0,X1)
& ~ moref(X0,X1) ) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
( ~ eq(pf(x,z),pf(y,u))
& ~ moref(pf(x,z),pf(y,u)) ),
inference(ennf_transformation,[],[f8]) ).
tff(f22,plain,
( eq(x,y)
| moref(x,y) ),
inference(cnf_transformation,[],[f12]) ).
tff(f23,plain,
( eq(z,u)
| moref(z,u) ),
inference(cnf_transformation,[],[f13]) ).
tff(f25,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ~ eq(X2,X3)
| eq(pf(X0,X2),pf(X1,X3))
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f27,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ~ eq(X2,X3)
| moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f28,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ~ moref(X2,X3)
| moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f29,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ~ eq(X0,X1)
| ~ moref(X2,X3)
| moref(pf(X0,X2),pf(X1,X3)) ),
inference(cnf_transformation,[],[f20]) ).
tff(f30,plain,
~ moref(pf(x,z),pf(y,u)),
inference(cnf_transformation,[],[f21]) ).
tff(f31,plain,
~ eq(pf(x,z),pf(y,u)),
inference(cnf_transformation,[],[f21]) ).
tff(f35,definition,
( spl0_1
<=> moref(z,u) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f37,plain,
( moref(z,u)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f39,definition,
( spl0_2
<=> eq(z,u) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f41,plain,
( eq(z,u)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f23,f39,f35]) ).
tff(f44,definition,
( spl0_3
<=> moref(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f46,plain,
( moref(x,y)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f48,definition,
( spl0_4
<=> eq(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f50,plain,
( eq(x,y)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f51,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f22,f48,f44]) ).
tff(f87,plain,
( ! [X0: frac,X1: frac] :
( ~ moref(X0,X1)
| moref(pf(X0,z),pf(X1,u)) )
| ~ spl0_2 ),
inference(resolution,[],[f27,f41]) ).
tff(f92,plain,
( moref(pf(x,z),pf(y,u))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f87,f46]) ).
tff(f93,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f92,f30]) ).
tff(f94,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f93]) ).
tff(f95,plain,
( ! [X0: frac,X1: frac] :
( ~ moref(X0,X1)
| moref(pf(X0,z),pf(X1,u)) )
| ~ spl0_1 ),
inference(resolution,[],[f37,f28]) ).
tff(f98,plain,
( moref(pf(x,z),pf(y,u))
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f95,f46]) ).
tff(f100,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f98,f30]) ).
tff(f101,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f100]) ).
tff(f104,plain,
( ! [X0: frac,X1: frac] :
( ~ eq(X0,X1)
| eq(pf(X0,z),pf(X1,u)) )
| ~ spl0_2 ),
inference(resolution,[],[f41,f25]) ).
tff(f105,plain,
( ! [X0: frac,X1: frac] :
( ~ moref(X0,X1)
| moref(pf(x,X0),pf(y,X1)) )
| ~ spl0_4 ),
inference(resolution,[],[f50,f29]) ).
tff(f109,plain,
( eq(pf(x,z),pf(y,u))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f104,f50]) ).
tff(f110,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f109,f31]) ).
tff(f111,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f110]) ).
tff(f113,plain,
( moref(pf(x,z),pf(y,u))
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f105,f37]) ).
tff(f114,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f113,f30]) ).
tff(f115,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f114]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f94]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f101]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f111]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f115]) ).
cnf(s7,plain,
~ spl0_2,
inference(rat,[],[s2,s3,s5]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s1,s7]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s4,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s9,s10]) ).
tff(f116,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM765_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 % Computer : n007.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 21:18:10 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.45 Running first-order model finding
% 0.13/0.45 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
% 0.18/0.49 % (1789623)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (1789633)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=387513866:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (1789633) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1789623-1789633"...
% 0.18/0.49 % (1789633)...printing done.
% 0.18/0.49 % (1789629)% WARNING: option uhcvi not known.
% 0.18/0.49 % (1789633)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (1789633)------------------------------
% 0.18/0.49 % (1789633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (1789633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (1789633)CaDiCaL version: 2.1.3
% 0.18/0.49 % (1789633)Termination reason: Refutation
% 0.18/0.49 % (1789633)Time elapsed: 0.002 s
% 0.18/0.49 % (1789633)Peak memory usage: 12 MB
% 0.18/0.49 % (1789633)Instructions burned: 4 (million)
% 0.18/0.49 % (1789623)Success in time 0.028 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------