%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM761_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:16:54 PM UTC 2026
% Result : Theorem 3.91s 1.59s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 13 unt; 0 typ; 3 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 32 ~; 26 |; 0 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?; 34 :)
% 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(pred_def_3,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(f1,axiom,
( ~ moref(x,y)
=> eq(x,y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
tff(f2,axiom,
moref(z,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
tff(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/sandbox/benchmark/theBenchmark.p',satz62g) ).
tff(f5,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(X0,X1)
=> ( moref(X2,X3)
=> moref(pf(X0,X2),pf(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz64) ).
tff(f6,conjecture,
moref(pf(x,z),pf(y,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65a) ).
tff(f7,negated_conjecture,
~ moref(pf(x,z),pf(y,u)),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f11,plain,
~ moref(pf(x,z),pf(y,u)),
inference(flattening,[],[f7]) ).
tff(f12,plain,
( eq(x,y)
| moref(x,y) ),
inference(ennf_transformation,[],[f1]) ).
tff(f14,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X2,X3)
| ~ eq(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f15,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X2,X3)
| ~ eq(X0,X1) ),
inference(flattening,[],[f14]) ).
tff(f16,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X2,X3)
| ~ moref(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f17,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X2,X3)
| ~ moref(X0,X1) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
( eq(x,y)
| moref(x,y) ),
inference(cnf_transformation,[],[f12]) ).
tff(f19,plain,
moref(z,u),
inference(cnf_transformation,[],[f2]) ).
tff(f21,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,[],[f15]) ).
tff(f22,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X2,X3)
| ~ moref(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f23,plain,
~ moref(pf(x,z),pf(y,u)),
inference(cnf_transformation,[],[f11]) ).
tff(f34,definition,
( spl1_1
<=> moref(x,y) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f37,definition,
( spl1_2
<=> eq(x,y) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f38,plain,
( eq(x,y)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f37]) ).
tff(f39,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f18,f37,f34]) ).
tff(f42,plain,
( ! [X0: frac,X1: frac] :
( moref(pf(x,X0),pf(y,X1))
| ~ moref(X0,X1) )
| ~ spl1_2 ),
inference(resolution,[],[f21,f38]) ).
tff(f43,plain,
( ~ moref(z,u)
| ~ spl1_2 ),
inference(resolution,[],[f42,f23]) ).
tff(f44,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f43,f19]) ).
tff(f45,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f44]) ).
tff(f47,plain,
( ~ moref(z,u)
| ~ moref(x,y) ),
inference(resolution,[],[f22,f23]) ).
tff(f50,definition,
( spl1_3
<=> moref(z,u) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f51,plain,
( ~ moref(z,u)
| spl1_3 ),
inference(avatar_component_clause,[],[f50]) ).
tff(f52,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f47,f50,f34]) ).
tff(f53,plain,
( $false
| spl1_3 ),
inference(resolution,[],[f51,f19]) ).
tff(f54,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f53]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
spl1_3,
inference(sat_conversion,[],[f54]) ).
cnf(s5,plain,
~ spl1_1,
inference(rat,[],[s3,s4]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s5]) ).
tff(f55,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM761_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n001.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 21:25:31 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.91/1.59 % (3959172)Detected formulas, will run a generic FOF schedule.
% 3.91/1.59 % (3959280)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2528763258:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.91/1.59 % (3959279)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2668537285:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.91/1.59 % (3959283)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1166205160:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.91/1.59 % (3959281)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1931137223:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.91/1.59 % (3959284)dis-21_1_sil=8000:lcm=predicate:random_seed=4086129429:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.91/1.59 % (3959278)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3423500619:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.91/1.59 % (3959281)Refutation not found, incomplete strategy
% 3.91/1.59 % (3959281)------------------------------
% 3.91/1.59 % (3959281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.59 % (3959281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.59 % (3959281)CaDiCaL version: 2.1.3
% 3.91/1.59 % (3959281)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.59 % (3959281)Time elapsed: 0.001 s
% 3.91/1.59 % (3959281)Peak memory usage: 88 MB
% 3.91/1.59 % (3959283)Also succeeded, but the first one will report.
% 3.91/1.59 % (3959284)First to succeed.
% 3.91/1.59 % (3959284)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3959172"
% 3.91/1.59 % (3959282)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4217375918:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.91/1.59 % (3959282)Also succeeded, but the first one will report.
% 3.91/1.59 % (3959281)------------------------------
% 3.91/1.59 % (3959281)------------------------------
% 3.91/1.59 % (3959284)Refutation found. Thanks to Tanya!
% 3.91/1.59 % SZS status Theorem for theBenchmark
% 3.91/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.59 % (3959284)------------------------------
% 3.91/1.59 % (3959284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.59 % (3959284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.59 % (3959284)CaDiCaL version: 2.1.3
% 3.91/1.59 % (3959284)Termination reason: Refutation
% 3.91/1.59 % (3959284)Time elapsed: 0.002 s
% 3.91/1.59 % (3959284)Peak memory usage: 89 MB
% 3.91/1.59 % (3959284)Instructions burned: 1 (million)
% 3.91/1.59 % (3959284)------------------------------
% 3.91/1.59 % (3959284)------------------------------
% 3.91/1.59 % (3959172)Success in time 0.471 s
% 3.91/1.59 % Vampire exiting
%------------------------------------------------------------------------------