%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM755_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 : 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 : Tue Sep 29 12:16:51 PM UTC 2026
% Result : Theorem 3.53s 1.47s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 52 ~; 29 |; 4 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?; 55 :)
% 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,
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,
lessf: ( frac * frac ) > $o ).
tff(pred_def_4,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(f1,axiom,
moref(pf(x,z),pf(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
tff(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) ).
tff(f4,axiom,
! [X0: frac,X1: frac,X2: frac] :
( eq(X0,X1)
=> eq(pf(X0,X2),pf(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62b) ).
tff(f5,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) ).
tff(f6,axiom,
! [X0: frac,X1: frac] :
( ~ eq(X0,X1)
=> ( ~ moref(X0,X1)
=> lessf(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41a) ).
tff(f7,conjecture,
moref(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz63a) ).
tff(f8,negated_conjecture,
~ moref(x,y),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f12,plain,
! [X0: frac,X1: frac] :
~ ( ( eq(X0,X1)
=> ~ moref(X0,X1) )
=> ( ( moref(X0,X1)
=> ~ lessf(X0,X1) )
=> ~ ( lessf(X0,X1)
=> ~ eq(X0,X1) ) ) ),
inference(flattening,[],[f3]) ).
tff(f13,plain,
~ moref(x,y),
inference(flattening,[],[f8]) ).
tff(f15,plain,
! [X0: frac,X1: frac] :
( ( ~ eq(X0,X1)
| ~ lessf(X0,X1) )
& ( ~ lessf(X0,X1)
| ~ moref(X0,X1) )
& ( ~ moref(X0,X1)
| ~ eq(X0,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
tff(f16,plain,
! [X0: frac,X1: frac] :
( ( ~ eq(X0,X1)
| ~ lessf(X0,X1) )
& ( ~ lessf(X0,X1)
| ~ moref(X0,X1) )
& ( ~ moref(X0,X1)
| ~ eq(X0,X1) ) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
! [X0: frac,X1: frac,X2: frac] :
( eq(pf(X0,X2),pf(X1,X2))
| ~ eq(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f18,plain,
! [X0: frac,X1: frac,X2: frac] :
( lessf(pf(X0,X2),pf(X1,X2))
| ~ lessf(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f19,plain,
! [X0: frac,X1: frac] :
( lessf(X0,X1)
| moref(X0,X1)
| eq(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
tff(f20,plain,
! [X0: frac,X1: frac] :
( lessf(X0,X1)
| moref(X0,X1)
| eq(X0,X1) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
moref(pf(x,z),pf(y,z)),
inference(cnf_transformation,[],[f1]) ).
tff(f23,plain,
! [X0: frac,X1: frac] :
( ~ eq(X0,X1)
| ~ moref(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f24,plain,
! [X0: frac,X1: frac] :
( ~ lessf(X0,X1)
| ~ moref(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f26,plain,
! [X2: frac,X0: frac,X1: frac] :
( eq(pf(X0,X2),pf(X1,X2))
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f27,plain,
! [X2: frac,X0: frac,X1: frac] :
( lessf(pf(X0,X2),pf(X1,X2))
| ~ lessf(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f28,plain,
! [X0: frac,X1: frac] :
( lessf(X0,X1)
| moref(X0,X1)
| eq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f29,plain,
~ moref(x,y),
inference(cnf_transformation,[],[f13]) ).
tff(f44,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ eq(X0,X1)
| ~ moref(pf(X0,X2),pf(X1,X2)) ),
inference(resolution,[],[f26,f23]) ).
tff(f46,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ lessf(X0,X1)
| ~ moref(pf(X0,X2),pf(X1,X2)) ),
inference(resolution,[],[f27,f24]) ).
tff(f50,plain,
! [X2: frac,X0: frac,X1: frac] :
( eq(X0,X2)
| moref(X0,X2)
| ~ moref(pf(X0,X1),pf(X2,X1)) ),
inference(resolution,[],[f46,f28]) ).
tff(f53,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( moref(X0,X1)
| ~ moref(pf(X0,X2),pf(X1,X2))
| ~ moref(pf(X0,X3),pf(X1,X3)) ),
inference(resolution,[],[f50,f44]) ).
tff(f62,plain,
! [X0: frac,X1: frac] :
( ~ moref(pf(x,X0),pf(y,X0))
| ~ moref(pf(x,X1),pf(y,X1)) ),
inference(resolution,[],[f53,f29]) ).
tff(f64,definition,
( spl1_1
<=> ! [X1: frac] : ~ moref(pf(x,X1),pf(y,X1)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f65,plain,
( ! [X1: frac] : ~ moref(pf(x,X1),pf(y,X1))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f66,plain,
( spl1_1
| spl1_1 ),
inference(avatar_split_clause,[],[f62,f64,f64]) ).
tff(f67,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f65,f21]) ).
tff(f69,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f67]) ).
cnf(s1,plain,
( spl1_1
| spl1_1 ),
inference(sat_conversion,[],[f66]) ).
cnf(s2,plain,
spl1_1,
inference(rat,[],[s1]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f69]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
tff(f70,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM755_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 21:17:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.53/1.47 % (3321289)Detected formulas, will run a generic FOF schedule.
% 3.53/1.47 % (3321297)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2222365108:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.47 % (3321297)Refutation not found, incomplete strategy
% 3.53/1.47 % (3321297)------------------------------
% 3.53/1.47 % (3321297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.47 % (3321297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.47 % (3321297)CaDiCaL version: 2.1.3
% 3.53/1.47 % (3321297)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.47 % (3321297)Time elapsed: 0.0000 s
% 3.53/1.47 % (3321297)Peak memory usage: 87 MB
% 3.53/1.47 % (3321294)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=4010961329:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.47 % (3321295)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=4232375562:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.47 % (3321296)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=3883832:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.47 % (3321300)dis-21_1_sil=8000:lcm=predicate:random_seed=3521275786: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)
% 3.53/1.47 % (3321298)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3661085084:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.47 % (3321299)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=814227597:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.47 % (3321298)Refutation not found, incomplete strategy
% 3.53/1.47 % (3321298)------------------------------
% 3.53/1.47 % (3321298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.47 % (3321298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.47 % (3321298)CaDiCaL version: 2.1.3
% 3.53/1.47 % (3321298)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.47 % (3321298)Time elapsed: 0.001 s
% 3.53/1.47 % (3321298)Peak memory usage: 87 MB
% 3.53/1.47 % (3321300)First to succeed.
% 3.53/1.47 % (3321299)Also succeeded, but the first one will report.
% 3.53/1.47 % (3321300)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3321289"
% 3.53/1.47 % (3321297)------------------------------
% 3.53/1.47 % (3321297)------------------------------
% 3.53/1.47 % (3321308)lrs+10_1_sil=8000:sp=occurrence:random_seed=1203150455:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.47 % (3321308)Also succeeded, but the first one will report.
% 3.53/1.47 % (3321298)------------------------------
% 3.53/1.47 % (3321298)------------------------------
% 3.53/1.47 % (3321300)Refutation found. Thanks to Tanya!
% 3.53/1.47 % SZS status Theorem for theBenchmark
% 3.53/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.47 % (3321300)------------------------------
% 3.53/1.47 % (3321300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.47 % (3321300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.47 % (3321300)CaDiCaL version: 2.1.3
% 3.53/1.47 % (3321300)Termination reason: Refutation
% 3.53/1.47 % (3321300)Time elapsed: 0.003 s
% 3.53/1.47 % (3321300)Peak memory usage: 89 MB
% 3.53/1.47 % (3321300)Instructions burned: 2 (million)
% 3.53/1.47 % (3321300)------------------------------
% 3.53/1.47 % (3321300)------------------------------
% 3.53/1.47 % (3321289)Success in time 0.416 s
% 3.53/1.47 % Vampire exiting
%------------------------------------------------------------------------------