%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM756_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 2.31s 0.93s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 79 ( 41 ~; 20 |; 4 &)
% ( 0 <=>; 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 0 ?; 43 :)
% 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,
eq: ( frac * frac ) > $o ).
tff(pred_def_2,type,
lessf: ( frac * frac ) > $o ).
tff(pred_def_3,type,
moref: ( frac * frac ) > $o ).
tff(f1,axiom,
eq(pf(x,z),pf(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
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/sandbox2/benchmark/theBenchmark.p',satz41b) ).
tff(f4,axiom,
! [X0: frac,X1: frac,X2: frac] :
( lessf(X0,X1)
=> lessf(pf(X0,X2),pf(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62c) ).
tff(f5,axiom,
! [X0: frac,X1: frac] :
( ~ eq(X0,X1)
=> ( ~ moref(X0,X1)
=> lessf(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41a) ).
tff(f6,axiom,
! [X0: frac,X1: frac,X2: frac] :
( moref(X0,X1)
=> moref(pf(X0,X2),pf(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62a) ).
tff(f7,conjecture,
eq(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63b) ).
tff(f8,negated_conjecture,
~ eq(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,
~ eq(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] :
( lessf(pf(X0,X2),pf(X1,X2))
| ~ lessf(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
tff(f18,plain,
! [X0: frac,X1: frac] :
( lessf(X0,X1)
| moref(X0,X1)
| eq(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f19,plain,
! [X0: frac,X1: frac] :
( lessf(X0,X1)
| moref(X0,X1)
| eq(X0,X1) ),
inference(flattening,[],[f18]) ).
tff(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( moref(pf(X0,X2),pf(X1,X2))
| ~ moref(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
tff(f21,plain,
eq(pf(x,z),pf(y,z)),
inference(cnf_transformation,[],[f1]) ).
tff(f23,plain,
! [X0: frac,X1: frac] :
( ~ moref(X0,X1)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f25,plain,
! [X0: frac,X1: frac] :
( ~ lessf(X0,X1)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f26,plain,
! [X2: frac,X0: frac,X1: frac] :
( lessf(pf(X0,X2),pf(X1,X2))
| ~ lessf(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f27,plain,
! [X0: frac,X1: frac] :
( lessf(X0,X1)
| moref(X0,X1)
| eq(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tff(f28,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ moref(X0,X1)
| moref(pf(X0,X2),pf(X1,X2)) ),
inference(cnf_transformation,[],[f20]) ).
tff(f29,plain,
~ eq(x,y),
inference(cnf_transformation,[],[f13]) ).
tff(f42,plain,
! [X2: frac,X0: frac,X1: frac] :
( ~ eq(pf(X0,X2),pf(X1,X2))
| ~ lessf(X0,X1) ),
inference(resolution,[],[f26,f25]) ).
tff(f45,plain,
~ lessf(x,y),
inference(resolution,[],[f42,f21]) ).
tff(f46,plain,
( moref(x,y)
| eq(x,y) ),
inference(resolution,[],[f45,f27]) ).
tff(f47,plain,
moref(x,y),
inference(forward_subsumption_resolution,[],[f46,f29]) ).
tff(f48,plain,
! [X0: frac] : moref(pf(x,X0),pf(y,X0)),
inference(resolution,[],[f47,f28]) ).
tff(f53,plain,
! [X0: frac] : ~ eq(pf(x,X0),pf(y,X0)),
inference(resolution,[],[f48,f23]) ).
tff(f56,plain,
$false,
inference(resolution,[],[f53,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM756_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 21:18:04 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.31/0.93 % (2755892)Detected formulas, will run a generic FOF schedule.
% 2.31/0.93 % (2755900)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3921627840:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.31/0.93 % (2755897)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=2890649984:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.31/0.93 % (2755902)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=993775020:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.31/0.93 % (2755898)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=142178388:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.31/0.93 % (2755899)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=3863623560:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.31/0.93 % (2755903)dis-21_1_sil=8000:lcm=predicate:random_seed=4279685039: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)
% 2.31/0.93 % (2755901)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=591308759:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.31/0.93 % (2755901)Refutation not found, incomplete strategy
% 2.31/0.93 % (2755901)------------------------------
% 2.31/0.93 % (2755901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.93 % (2755901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.93 % (2755900)Refutation not found, incomplete strategy
% 2.31/0.93 % (2755900)------------------------------
% 2.31/0.93 % (2755900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.93 % (2755901)CaDiCaL version: 2.1.3
% 2.31/0.93 % (2755901)Termination reason: Refutation not found, incomplete strategy
% 2.31/0.93 % (2755901)Time elapsed: 0.0000 s
% 2.31/0.93 % (2755900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.93 % (2755901)Peak memory usage: 86 MB
% 2.31/0.93 % (2755900)CaDiCaL version: 2.1.3
% 2.31/0.93 % (2755900)Termination reason: Refutation not found, incomplete strategy
% 2.31/0.93 % (2755900)Time elapsed: 0.0000 s
% 2.31/0.93 % (2755900)Peak memory usage: 86 MB
% 2.31/0.93 % (2755902)First to succeed.
% 2.31/0.93 % (2755903)Also succeeded, but the first one will report.
% 2.31/0.93 % (2755902)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2755892"
% 2.31/0.93 % (2755901)------------------------------
% 2.31/0.93 % (2755901)------------------------------
% 2.31/0.93 % (2755900)------------------------------
% 2.31/0.93 % (2755900)------------------------------
% 2.31/0.93 % (2755902)Refutation found. Thanks to Tanya!
% 2.31/0.93 % SZS status Theorem for theBenchmark
% 2.31/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/0.93 % (2755902)------------------------------
% 2.31/0.93 % (2755902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.93 % (2755902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.93 % (2755902)CaDiCaL version: 2.1.3
% 2.31/0.93 % (2755902)Termination reason: Refutation
% 2.31/0.93 % (2755902)Time elapsed: 0.002 s
% 2.31/0.93 % (2755902)Peak memory usage: 88 MB
% 2.31/0.93 % (2755902)Instructions burned: 2 (million)
% 2.31/0.93 % (2755902)------------------------------
% 2.31/0.93 % (2755902)------------------------------
% 2.31/0.93 % (2755892)Success in time 0.296 s
% 2.31/0.93 % Vampire exiting
%------------------------------------------------------------------------------