%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD070-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:49:20 AM UTC 2026
% Result : Unsatisfiable 4.16s 1.38s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 68 ( 20 unt; 5 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 144 ( 69 ~; 70 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f16,axiom,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_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/sandbox2/benchmark/theBenchmark.p',totality_of_order_relation) ).
fof(f19,axiom,
! [X2,X0,X1] :
( less_or_equal(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ less_or_equal(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f22,axiom,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1)
| ~ equalish(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
fof(f29,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f31,negated_conjecture,
equalish(add(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_equals_c_4) ).
fof(f32,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_5) ).
fof(f33,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_6) ).
fof(f34,negated_conjecture,
~ less_or_equal(additive_identity,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_7) ).
fof(f35,plain,
equalish(c,add(a,b)),
inference(resolution,[],[f22,f31]) ).
fof(f61,plain,
! [X0] :
( ~ less_or_equal(X0,additive_identity)
| less_or_equal(X0,b) ),
inference(resolution,[],[f17,f33]) ).
fof(f62,plain,
! [X0] :
( ~ equalish(X0,add(a,b))
| equalish(X0,c) ),
inference(resolution,[],[f23,f31]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ equalish(X0,X2)
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X0) ),
inference(resolution,[],[f18,f26]) ).
fof(f81,plain,
! [X0] :
( less_or_equal(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[],[f18]) ).
fof(f82,plain,
! [X0] :
( less_or_equal(X0,X0)
| ~ defined(X0) ),
inference(duplicate_literal_removal,[],[f81]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ equalish(add(X1,X0),X3)
| ~ less_or_equal(X1,X2)
| less_or_equal(X3,add(X2,X0))
| ~ defined(X0) ),
inference(resolution,[],[f19,f26]) ).
fof(f135,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| less_or_equal(X1,X0)
| ~ defined(X0) ),
inference(resolution,[],[f82,f26]) ).
fof(f179,plain,
! [X0] :
( ~ defined(c)
| ~ defined(X0)
| less_or_equal(add(a,b),X0)
| less_or_equal(X0,c) ),
inference(resolution,[],[f75,f35]) ).
fof(f183,plain,
! [X0] :
( less_or_equal(add(a,b),X0)
| ~ defined(X0)
| less_or_equal(X0,c) ),
inference(forward_subsumption_resolution,[],[f179,f30]) ).
fof(f232,plain,
! [X0,X1] :
( ~ less_or_equal(additive_identity,X0)
| less_or_equal(X1,add(X0,X1))
| ~ defined(X1)
| ~ defined(X1) ),
inference(resolution,[],[f94,f2]) ).
fof(f242,plain,
! [X0,X1] :
( less_or_equal(X1,add(X0,X1))
| ~ less_or_equal(additive_identity,X0)
| ~ defined(X1) ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f359,definition,
( spl0_17
<=> less_or_equal(add(a,b),b) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f361,plain,
( less_or_equal(add(a,b),b)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f453,definition,
( spl0_22
<=> equalish(c,b) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f455,plain,
( equalish(c,b)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f462,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_identity,c)
| less_or_equal(add(a,b),b) ),
inference(resolution,[],[f183,f61]) ).
fof(f467,plain,
( less_or_equal(additive_identity,c)
| less_or_equal(add(a,b),b) ),
inference(forward_subsumption_resolution,[],[f462,f11]) ).
fof(f470,plain,
less_or_equal(add(a,b),b),
inference(forward_subsumption_resolution,[],[f467,f34]) ).
fof(f472,plain,
spl0_17,
inference(avatar_split_clause,[],[f470,f359]) ).
fof(f498,plain,
( ~ less_or_equal(b,add(a,b))
| equalish(b,add(a,b))
| ~ spl0_17 ),
inference(resolution,[],[f361,f16]) ).
fof(f500,definition,
( spl0_25
<=> equalish(b,add(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f502,plain,
( equalish(b,add(a,b))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f504,definition,
( spl0_26
<=> less_or_equal(b,add(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f506,plain,
( ~ less_or_equal(b,add(a,b))
| spl0_26 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f507,plain,
( spl0_25
| ~ spl0_26
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f498,f359,f504,f500]) ).
fof(f649,plain,
( ~ less_or_equal(additive_identity,a)
| ~ defined(b)
| spl0_26 ),
inference(resolution,[],[f506,f242]) ).
fof(f650,plain,
( ~ defined(b)
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f649,f32]) ).
fof(f652,plain,
( $false
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f650,f29]) ).
fof(f653,plain,
spl0_26,
inference(avatar_contradiction_clause,[],[f652]) ).
fof(f676,definition,
( spl0_29
<=> equalish(b,c) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f678,plain,
( equalish(b,c)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f699,plain,
( equalish(b,c)
| ~ spl0_25 ),
inference(resolution,[],[f502,f62]) ).
fof(f708,plain,
( spl0_29
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f699,f500,f676]) ).
fof(f725,plain,
( equalish(c,b)
| ~ spl0_29 ),
inference(resolution,[],[f678,f22]) ).
fof(f726,plain,
( spl0_22
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f725,f676,f453]) ).
fof(f743,plain,
( less_or_equal(b,c)
| ~ defined(c)
| ~ spl0_22 ),
inference(resolution,[],[f455,f135]) ).
fof(f748,plain,
( less_or_equal(b,c)
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f743,f30]) ).
fof(f791,plain,
( ! [X0] :
( ~ less_or_equal(X0,b)
| less_or_equal(X0,c) )
| ~ spl0_22 ),
inference(resolution,[],[f748,f17]) ).
fof(f2668,plain,
( less_or_equal(additive_identity,c)
| ~ spl0_22 ),
inference(resolution,[],[f791,f33]) ).
fof(f2671,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f2668,f34]) ).
fof(f2672,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f2671]) ).
cnf(s18,plain,
spl0_17,
inference(sat_conversion,[],[f472]) ).
cnf(s20,plain,
( ~ spl0_17
| spl0_25
| ~ spl0_26 ),
inference(sat_conversion,[],[f507]) ).
cnf(s22,plain,
spl0_26,
inference(sat_conversion,[],[f653]) ).
cnf(s24,plain,
( ~ spl0_25
| spl0_29 ),
inference(sat_conversion,[],[f708]) ).
cnf(s25,plain,
( spl0_22
| ~ spl0_29 ),
inference(sat_conversion,[],[f726]) ).
cnf(s47,plain,
~ spl0_22,
inference(sat_conversion,[],[f2672]) ).
cnf(s53,plain,
~ spl0_29,
inference(rat,[],[s25,s47]) ).
cnf(s54,plain,
~ spl0_25,
inference(rat,[],[s24,s53]) ).
cnf(s56,plain,
~ spl0_17,
inference(rat,[],[s20,s22,s54]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s18,s56]) ).
fof(f2681,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD070-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 00:50:58 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.78/1.16 % (2190900)Input is clausal, will run a generic CNF schedule.
% 3.78/1.16 % (2190911)dis-21_1_sil=8000:lcm=predicate:random_seed=705785690: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)
% 3.78/1.16 % (2190911)Instruction limit reached!
% 3.78/1.16 % (2190911)------------------------------
% 3.78/1.16 % (2190911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.16 % (2190911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.16 % (2190911)CaDiCaL version: 2.1.3
% 3.78/1.16 % (2190911)Termination reason: Instruction limit
% 3.78/1.16 % (2190911)Termination phase: Saturation
% 3.78/1.16 % (2190911)Time elapsed: 0.029 s
% 3.78/1.16 % (2190911)Peak memory usage: 88 MB
% 3.78/1.16 % (2190911)Instructions burned: 119 (million)
% 3.78/1.16 % (2190910)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3336862986:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.78/1.16 % (2190908)lrs+10_1_sil=8000:sp=occurrence:random_seed=3508858939:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.78/1.16 % (2190909)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1524557460:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.78/1.16 % (2190905)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=433714131:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.78/1.16 % (2190906)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=177195154:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.78/1.16 % (2190907)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2055031593:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.78/1.16 % (2190909)Instruction limit reached!
% 3.78/1.16 % (2190909)------------------------------
% 3.78/1.16 % (2190909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.16 % (2190909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.16 % (2190909)CaDiCaL version: 2.1.3
% 3.78/1.16 % (2190909)Termination reason: Instruction limit
% 3.78/1.16 % (2190909)Termination phase: Saturation
% 3.78/1.16 % (2190909)Time elapsed: 0.066 s
% 3.78/1.16 % (2190909)Peak memory usage: 88 MB
% 3.78/1.16 % (2190909)Instructions burned: 114 (million)
% 3.78/1.16 % (2190908)First to succeed.
% 3.78/1.16 % (2190908)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2190900"
% 3.78/1.16 % (2190913)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2178498381:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.78/1.16 % (2190910)Instruction limit reached!
% 3.78/1.16 % (2190910)------------------------------
% 3.78/1.16 % (2190910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.16 % (2190910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.16 % (2190910)CaDiCaL version: 2.1.3
% 3.78/1.16 % (2190910)Termination reason: Instruction limit
% 3.78/1.16 % (2190910)Termination phase: Saturation
% 3.78/1.16 % (2190910)Time elapsed: 0.125 s
% 3.78/1.16 % (2190910)Peak memory usage: 89 MB
% 3.78/1.16 % (2190910)Instructions burned: 181 (million)
% 3.78/1.16 % (2190913)Instruction limit reached!
% 3.78/1.16 % (2190913)------------------------------
% 3.78/1.16 % (2190913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.16 % (2190913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.16 % (2190913)CaDiCaL version: 2.1.3
% 3.78/1.16 % (2190913)Termination reason: Instruction limit
% 3.78/1.16 % (2190913)Termination phase: Saturation
% 3.78/1.16 % (2190913)Time elapsed: 0.046 s
% 3.78/1.16 % (2190913)Peak memory usage: 89 MB
% 3.78/1.16 % (2190913)Instructions burned: 143 (million)
% 3.78/1.16 % (2190920)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4088528302:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.78/1.16 % (2190922)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1946660703:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.78/1.16 % (2190920)Instruction limit reached!
% 3.78/1.16 % (2190920)------------------------------
% 4.16/1.38 % (2190920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.16/1.38 % (2190920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.38 % (2190920)CaDiCaL version: 2.1.3
% 4.16/1.38 % (2190920)Termination reason: Instruction limit
% 4.16/1.38 % (2190920)Termination phase: Saturation
% 4.16/1.38 % (2190920)Time elapsed: 0.096 s
% 4.16/1.38 % (2190920)Peak memory usage: 94 MB
% 4.16/1.38 % (2190920)Instructions burned: 191 (million)
% 4.16/1.38 % (2190922)Instruction limit reached!
% 4.16/1.38 % (2190922)------------------------------
% 4.16/1.38 % (2190922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.16/1.38 % (2190922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.38 % (2190922)CaDiCaL version: 2.1.3
% 4.16/1.38 % (2190922)Termination reason: Instruction limit
% 4.16/1.38 % (2190922)Termination phase: Saturation
% 4.16/1.38 % (2190922)Time elapsed: 0.063 s
% 4.16/1.38 % (2190922)Peak memory usage: 88 MB
% 4.16/1.38 % (2190922)Instructions burned: 221 (million)
% 4.16/1.38 % (2190923)lrs+10_64_to=lpo:sil=8000:random_seed=2810196430:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.16/1.38 % (2190908)Refutation found. Thanks to Tanya!
% 4.16/1.38 % SZS status Unsatisfiable for theBenchmark
% 4.16/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 4.16/1.38 % (2190908)------------------------------
% 4.16/1.38 % (2190908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.16/1.38 % (2190908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.38 % (2190908)CaDiCaL version: 2.1.3
% 4.16/1.38 % (2190908)Termination reason: Refutation
% 4.16/1.38 % (2190908)Time elapsed: 0.069 s
% 4.16/1.38 % (2190908)Peak memory usage: 90 MB
% 4.16/1.38 % (2190908)Instructions burned: 105 (million)
% 4.16/1.38 % (2190908)------------------------------
% 4.16/1.38 % (2190908)------------------------------
% 4.16/1.38 % (2190900)Success in time 0.499 s
% 4.16/1.38 % Vampire exiting
%------------------------------------------------------------------------------