%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD055-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 09:49:15 AM UTC 2026
% Result : Unsatisfiable 3.58s 1.19s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 51 ( 16 unt; 4 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 110 ( 57 ~; 49 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f18,axiom,
! [X0,X1] :
( less_or_equal(X1,X0)
| less_or_equal(X0,X1)
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
fof(f22,axiom,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f26,axiom,
! [X2,X0,X1] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X2,X1)
| ~ equalish(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f30,axiom,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
fof(f31,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f32,negated_conjecture,
equalish(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_equals_c_5) ).
fof(f33,negated_conjecture,
~ less_or_equal(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_6) ).
fof(f48,plain,
! [X0] :
( ~ less_or_equal(X0,c)
| ~ equalish(X0,a) ),
inference(resolution,[],[f26,f33]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ less_or_equal(X1,X2)
| ~ equalish(X0,X2)
| ~ less_or_equal(X0,X1)
| equalish(X1,X2) ),
inference(resolution,[],[f26,f16]) ).
fof(f54,plain,
( less_or_equal(c,a)
| ~ defined(c)
| ~ defined(a) ),
inference(resolution,[],[f18,f33]) ).
fof(f61,plain,
( less_or_equal(c,a)
| ~ defined(a) ),
inference(forward_subsumption_resolution,[],[f54,f30]) ).
fof(f63,plain,
less_or_equal(c,a),
inference(forward_subsumption_resolution,[],[f61,f28]) ).
fof(f66,plain,
! [X0] :
( ~ equalish(X0,a)
| less_or_equal(c,X0)
| ~ defined(c)
| ~ defined(X0) ),
inference(resolution,[],[f48,f18]) ).
fof(f69,plain,
! [X0] :
( less_or_equal(c,X0)
| ~ equalish(X0,a)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[],[f66,f30]) ).
fof(f105,plain,
( ~ equalish(c,a)
| ~ defined(c)
| ~ equalish(c,a) ),
inference(resolution,[],[f69,f48]) ).
fof(f107,plain,
( ~ equalish(c,a)
| ~ defined(c) ),
inference(duplicate_literal_removal,[],[f105]) ).
fof(f108,plain,
~ equalish(c,a),
inference(forward_subsumption_resolution,[],[f107,f30]) ).
fof(f111,definition,
( spl0_3
<=> equalish(c,b) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f112,plain,
( ~ equalish(c,b)
| spl0_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_4
<=> equalish(c,a) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f115,plain,
( ~ equalish(c,a)
| spl0_4 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f132,definition,
( spl0_5
<=> equalish(a,b) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f133,plain,
( equalish(a,b)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f145,plain,
! [X0] :
( ~ equalish(X0,b)
| ~ less_or_equal(X0,a)
| equalish(a,b) ),
inference(resolution,[],[f50,f31]) ).
fof(f151,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f108,f114]) ).
fof(f156,plain,
( ~ equalish(b,c)
| spl0_3 ),
inference(resolution,[],[f112,f22]) ).
fof(f157,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f156,f32]) ).
fof(f158,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f157]) ).
fof(f165,plain,
( ~ equalish(a,c)
| spl0_4 ),
inference(resolution,[],[f115,f22]) ).
fof(f174,plain,
( ! [X0] :
( ~ equalish(a,X0)
| ~ equalish(X0,c) )
| spl0_4 ),
inference(resolution,[],[f165,f23]) ).
fof(f190,plain,
( ~ equalish(b,c)
| spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f174,f133]) ).
fof(f194,plain,
( $false
| spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f190,f32]) ).
fof(f195,plain,
( spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f197,definition,
( spl0_7
<=> ! [X0] :
( ~ equalish(X0,b)
| ~ less_or_equal(X0,a) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f198,plain,
( ! [X0] :
( ~ less_or_equal(X0,a)
| ~ equalish(X0,b) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f199,plain,
( spl0_5
| spl0_7 ),
inference(avatar_split_clause,[],[f145,f197,f132]) ).
fof(f209,plain,
( ~ equalish(c,b)
| ~ spl0_7 ),
inference(resolution,[],[f198,f63]) ).
fof(f212,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f209,f197,f111]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f151]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f158]) ).
cnf(s7,plain,
( spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f195]) ).
cnf(s8,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f199]) ).
cnf(s9,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f212]) ).
cnf(s11,plain,
~ spl0_7,
inference(rat,[],[s9,s6]) ).
cnf(s12,plain,
spl0_5,
inference(rat,[],[s8,s11]) ).
cnf(s13,plain,
spl0_4,
inference(rat,[],[s7,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s5,s13]) ).
fof(f215,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD055-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n017.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 00:38:22 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 3.58/1.19 % (11274)Input is clausal, will run a generic CNF schedule.
% 3.58/1.19 % (11281)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=25538881:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.58/1.19 % (11284)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3000315040:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.58/1.19 % (11280)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2059829586:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.58/1.19 % (11279)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=3561785829:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.58/1.19 % (11283)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3590822344:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.58/1.19 % (11285)dis-21_1_sil=8000:lcm=predicate:random_seed=4140473854:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.58/1.19 % (11282)lrs+10_1_sil=8000:sp=occurrence:random_seed=2433314079:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.58/1.19 % (11283)First to succeed.
% 3.58/1.19 % (11283)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11274"
% 3.58/1.19 % (11282)Also succeeded, but the first one will report.
% 3.58/1.19 % (11285)Also succeeded, but the first one will report.
% 3.58/1.19 % (11284)Also succeeded, but the first one will report.
% 3.58/1.19 % (11283)Refutation found. Thanks to Tanya!
% 3.58/1.19 % SZS status Unsatisfiable for theBenchmark
% 3.58/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.19 % (11283)------------------------------
% 3.58/1.19 % (11283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.19 % (11283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.19 % (11283)CaDiCaL version: 2.1.3
% 3.58/1.19 % (11283)Termination reason: Refutation
% 3.58/1.19 % (11283)Time elapsed: 0.005 s
% 3.58/1.19 % (11283)Peak memory usage: 89 MB
% 3.58/1.19 % (11283)Instructions burned: 5 (million)
% 3.58/1.19 % (11283)------------------------------
% 3.58/1.19 % (11283)------------------------------
% 3.58/1.19 % (11274)Success in time 0.435 s
% 3.58/1.19 % Vampire exiting
%------------------------------------------------------------------------------