%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS003_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 11:41:26 AM UTC 2026
% Result : Theorem 3.48s 1.36s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 99 ( 50 ~; 38 |; 4 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 42 ( 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
unreal: $tType ).
tff(type_def_6,type,
real: $tType ).
tff(func_def_0,type,
u1r1: unreal > real ).
tff(func_def_1,type,
u1r2: unreal > real ).
tff(func_def_2,type,
u3r1: unreal > real ).
tff(func_def_3,type,
u3r2: unreal > real ).
tff(func_def_4,type,
exist: unreal ).
tff(pred_def_1,type,
f: unreal > $o ).
tff(pred_def_2,type,
d: unreal > $o ).
tff(pred_def_3,type,
e: unreal > $o ).
tff(pred_def_4,type,
s1most: unreal > $o ).
tff(pred_def_5,type,
s: ( unreal * real ) > $o ).
tff(pred_def_6,type,
c: unreal > $o ).
tff(pred_def_7,type,
equalish: ( real * real ) > $o ).
tff(pred_def_8,type,
s2least: unreal > $o ).
tff(f1,axiom,
! [X0: unreal] :
( c(X0)
=> s2least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(f3,axiom,
! [X0: unreal] :
~ ( s2least(X0)
& equalish(u1r2(X0),u1r1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(f4,axiom,
! [X0: unreal] :
( s2least(X0)
=> s(X0,u1r1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(f5,axiom,
! [X0: unreal] :
( s2least(X0)
=> s(X0,u1r2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(f7,axiom,
! [X0: unreal] :
( d(X0)
=> s1most(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
tff(f9,axiom,
! [X0: real,X1: real,X2: unreal] :
( ( s1most(X2)
& s(X2,X1)
& s(X2,X0) )
=> equalish(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
tff(f13,axiom,
! [X0: unreal] :
( e(X0)
=> c(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
tff(f14,axiom,
! [X0: unreal] :
( f(X0)
=> d(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
tff(f15,conjecture,
( ~ e(exist)
| ~ f(exist) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1__clause_2) ).
tff(f16,negated_conjecture,
~ ( ~ e(exist)
| ~ f(exist) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f17,plain,
! [X0: unreal] :
( s2least(X0)
| ~ c(X0) ),
inference(ennf_transformation,[],[f1]) ).
tff(f19,plain,
! [X0: unreal] :
( ~ s2least(X0)
| ~ equalish(u1r2(X0),u1r1(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f20,plain,
! [X0: unreal] :
( s(X0,u1r1(X0))
| ~ s2least(X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f21,plain,
! [X0: unreal] :
( s(X0,u1r2(X0))
| ~ s2least(X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f24,plain,
! [X0: unreal] :
( s1most(X0)
| ~ d(X0) ),
inference(ennf_transformation,[],[f7]) ).
tff(f26,plain,
! [X0: real,X1: real,X2: unreal] :
( equalish(X1,X0)
| ~ s1most(X2)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f27,plain,
! [X0: real,X1: real,X2: unreal] :
( equalish(X1,X0)
| ~ s1most(X2)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(flattening,[],[f26]) ).
tff(f29,plain,
! [X0: unreal] :
( c(X0)
| ~ e(X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f30,plain,
! [X0: unreal] :
( d(X0)
| ~ f(X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f31,plain,
( e(exist)
& f(exist) ),
inference(ennf_transformation,[],[f16]) ).
tff(f32,plain,
! [X0: unreal] :
( s2least(X0)
| ~ c(X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f34,plain,
! [X0: unreal] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f35,plain,
! [X0: unreal] :
( s(X0,u1r1(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[],[f20]) ).
tff(f36,plain,
! [X0: unreal] :
( s(X0,u1r2(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[],[f21]) ).
tff(f38,plain,
! [X0: unreal] :
( s1most(X0)
| ~ d(X0) ),
inference(cnf_transformation,[],[f24]) ).
tff(f40,plain,
! [X2: unreal,X0: real,X1: real] :
( ~ s1most(X2)
| equalish(X1,X0)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f44,plain,
! [X0: unreal] :
( c(X0)
| ~ e(X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f45,plain,
! [X0: unreal] :
( d(X0)
| ~ f(X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f46,plain,
f(exist),
inference(cnf_transformation,[],[f31]) ).
tff(f47,plain,
e(exist),
inference(cnf_transformation,[],[f31]) ).
tff(f48,plain,
! [X2: unreal,X0: real,X1: real] :
( ~ d(X2)
| ~ s(X2,X0)
| ~ s(X2,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f40,f38]) ).
tff(f50,plain,
! [X2: real,X0: unreal,X1: real] :
( ~ f(X0)
| ~ s(X0,X2)
| equalish(X1,X2)
| ~ s(X0,X1) ),
inference(resolution,[],[f48,f45]) ).
tff(f51,plain,
! [X0: real,X1: real] :
( equalish(X1,X0)
| ~ s(exist,X0)
| ~ s(exist,X1) ),
inference(resolution,[],[f50,f46]) ).
tff(f52,plain,
! [X0: unreal] :
( ~ s(exist,u1r2(X0))
| ~ s(exist,u1r1(X0))
| ~ s2least(X0) ),
inference(resolution,[],[f51,f34]) ).
tff(f54,plain,
( ~ s(exist,u1r1(exist))
| ~ s2least(exist)
| ~ s2least(exist) ),
inference(resolution,[],[f52,f36]) ).
tff(f55,plain,
( ~ s(exist,u1r1(exist))
| ~ s2least(exist) ),
inference(duplicate_literal_removal,[],[f54]) ).
tff(f56,plain,
~ s2least(exist),
inference(forward_subsumption_resolution,[],[f55,f35]) ).
tff(f58,plain,
~ c(exist),
inference(resolution,[],[f56,f32]) ).
tff(f64,plain,
~ e(exist),
inference(resolution,[],[f58,f44]) ).
tff(f65,plain,
$false,
inference(forward_subsumption_resolution,[],[f64,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS003_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 % Computer : n014.cluster.edu
% 0.21/0.50 % Model : x86_64 x86_64
% 0.21/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.50 % Memory : 8046.5625MB
% 0.21/0.50 % OS : Linux 6.8.0-71-generic
% 0.21/0.50 % CPULimit : 300
% 0.21/0.50 % WCLimit : 300
% 0.21/0.50 % DateTime : Sun Sep 27 13:15:02 UTC 2026
% 0.21/0.50 % CPUTime :
% 0.21/0.50 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.53 Running first-order theorem proving
% 0.21/0.53 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
% 3.48/1.36 % (810343)Detected formulas, will run a generic FOF schedule.
% 3.48/1.36 % (810354)dis-21_1_sil=8000:lcm=predicate:random_seed=3455107744: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)
% 3.48/1.36 % (810350)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=978004409:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.36 % (810352)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1413392216:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.36 % (810348)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=3843660541:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.36 % (810349)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=1811375034:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.36 % (810353)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2140507085:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.36 % (810351)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2313969113:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.36 % (810351)Refutation not found, incomplete strategy
% 3.48/1.36 % (810351)------------------------------
% 3.48/1.36 % (810351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.36 % (810352)Refutation not found, incomplete strategy
% 3.48/1.36 % (810352)------------------------------
% 3.48/1.36 % (810352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.36 % (810351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.36 % (810352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.36 % (810351)CaDiCaL version: 2.1.3
% 3.48/1.36 % (810352)CaDiCaL version: 2.1.3
% 3.48/1.36 % (810351)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.36 % (810351)Time elapsed: 0.0000 s
% 3.48/1.36 % (810352)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.36 % (810352)Time elapsed: 0.001 s
% 3.48/1.36 % (810351)Peak memory usage: 86 MB
% 3.48/1.36 % (810352)Peak memory usage: 87 MB
% 3.48/1.36 % (810353)First to succeed.
% 3.48/1.36 % (810354)Also succeeded, but the first one will report.
% 3.48/1.36 % (810353)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-810343"
% 3.48/1.36 % (810351)------------------------------
% 3.48/1.36 % (810351)------------------------------
% 3.48/1.36 % (810352)------------------------------
% 3.48/1.36 % (810352)------------------------------
% 3.48/1.36 % (810353)Refutation found. Thanks to Tanya!
% 3.48/1.36 % SZS status Theorem for theBenchmark
% 3.48/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.36 % (810353)------------------------------
% 3.48/1.36 % (810353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.36 % (810353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.36 % (810353)CaDiCaL version: 2.1.3
% 3.48/1.36 % (810353)Termination reason: Refutation
% 3.48/1.36 % (810353)Time elapsed: 0.003 s
% 3.48/1.36 % (810353)Peak memory usage: 88 MB
% 3.48/1.36 % (810353)Instructions burned: 2 (million)
% 3.48/1.36 % (810353)------------------------------
% 3.48/1.36 % (810353)------------------------------
% 3.48/1.36 % (810343)Success in time 0.429 s
% 3.48/1.36 % Vampire exiting
%------------------------------------------------------------------------------