%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM765_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 : n014.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 12:16:55 PM UTC 2026
% Result : Theorem 2.62s 1.33s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 137 ( 66 ~; 50 |; 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 : 52 ( 0 sgn 52 !; 0 ?; 52 :)
% 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/sandbox/benchmark/theBenchmark.p',m) ).
tff(f2,axiom,
( ~ moref(z,u)
=> eq(z,u) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',satz65a) ).
tff(f7,conjecture,
( ~ moref(pf(x,z),pf(y,u))
=> eq(pf(x,z),pf(y,u)) ),
file('/export/starexec/sandbox/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(f11,plain,
( ~ eq(pf(x,z),pf(y,u))
& ~ moref(pf(x,z),pf(y,u)) ),
inference(ennf_transformation,[],[f8]) ).
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(f14,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(f15,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,[],[f14]) ).
tff(f16,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(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(flattening,[],[f16]) ).
tff(f18,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(f19,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( eq(pf(X0,X2),pf(X1,X3))
| ~ eq(X2,X3)
| ~ eq(X0,X1) ),
inference(flattening,[],[f18]) ).
tff(f20,plain,
~ moref(pf(x,z),pf(y,u)),
inference(cnf_transformation,[],[f11]) ).
tff(f21,plain,
~ eq(pf(x,z),pf(y,u)),
inference(cnf_transformation,[],[f11]) ).
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] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ moref(X2,X3)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tff(f26,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(f27,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( moref(pf(X0,X2),pf(X1,X3))
| ~ eq(X2,X3)
| ~ moref(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f28,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( eq(pf(X0,X2),pf(X1,X3))
| ~ eq(X2,X3)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tff(f29,plain,
( ~ moref(z,u)
| ~ moref(x,y) ),
inference(resolution,[],[f20,f26]) ).
tff(f30,plain,
( ~ eq(z,u)
| ~ moref(x,y) ),
inference(resolution,[],[f20,f27]) ).
tff(f32,plain,
( ~ moref(z,u)
| ~ eq(x,y) ),
inference(resolution,[],[f20,f25]) ).
tff(f34,definition,
( spl0_1
<=> eq(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f36,plain,
( ~ eq(x,y)
| spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f38,definition,
( spl0_2
<=> moref(z,u) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f40,plain,
( ~ moref(z,u)
| spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f41,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f32,f38,f34]) ).
tff(f43,definition,
( spl0_3
<=> moref(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f45,plain,
( ~ moref(x,y)
| spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
tff(f48,definition,
( spl0_4
<=> eq(z,u) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f50,plain,
( ~ eq(z,u)
| spl0_4 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f51,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f30,f48,f43]) ).
tff(f52,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f29,f38,f43]) ).
tff(f53,plain,
( ~ eq(z,u)
| ~ eq(x,y) ),
inference(resolution,[],[f21,f28]) ).
tff(f54,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f53,f48,f34]) ).
tff(f55,plain,
( moref(x,y)
| spl0_1 ),
inference(resolution,[],[f36,f22]) ).
tff(f56,plain,
( $false
| spl0_1
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f55,f45]) ).
tff(f57,plain,
( spl0_1
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f56]) ).
tff(f58,plain,
( moref(z,u)
| spl0_4 ),
inference(resolution,[],[f50,f23]) ).
tff(f59,plain,
( $false
| spl0_2
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f58,f40]) ).
tff(f60,plain,
( spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s3,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f54]) ).
cnf(s6,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
( spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s8,plain,
~ spl0_3,
inference(rat,[],[s7,s3,s4]) ).
cnf(s9,plain,
spl0_1,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
~ spl0_4,
inference(rat,[],[s5,s9]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s1,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s7,s10,s11]) ).
tff(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM765_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 21:20:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.62/1.33 % (1180930)Detected formulas, will run a generic FOF schedule.
% 2.62/1.33 % (1180938)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3694074078:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.33 % (1180938)First to succeed.
% 2.62/1.33 % (1180938)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1180930"
% 2.62/1.33 % (1180935)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=1983323801:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.33 % (1180936)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=2437246450:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.33 % (1180937)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=1125715277:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.33 % (1180939)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1775893601:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.33 % (1180941)dis-21_1_sil=8000:lcm=predicate:random_seed=2228148853: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)
% 2.62/1.33 % (1180940)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2155852351:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.33 % (1180939)Also succeeded, but the first one will report.
% 2.62/1.33 % (1180941)Also succeeded, but the first one will report.
% 2.62/1.33 % (1180940)Also succeeded, but the first one will report.
% 2.62/1.33 % (1180938)Refutation found. Thanks to Tanya!
% 2.62/1.33 % SZS status Theorem for theBenchmark
% 2.62/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.33 % (1180938)------------------------------
% 2.62/1.33 % (1180938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.33 % (1180938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.33 % (1180938)CaDiCaL version: 2.1.3
% 2.62/1.33 % (1180938)Termination reason: Refutation
% 2.62/1.33 % (1180938)Time elapsed: 0.002 s
% 2.62/1.33 % (1180938)Peak memory usage: 89 MB
% 2.62/1.33 % (1180938)Instructions burned: 2 (million)
% 2.62/1.33 % (1180938)------------------------------
% 2.62/1.33 % (1180938)------------------------------
% 2.62/1.33 % (1180930)Success in time 0.287 s
% 2.62/1.33 % Vampire exiting
%------------------------------------------------------------------------------