%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD060-2 : 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 : n001.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 09:49:17 AM UTC 2026
% Result : Unsatisfiable 2.84s 0.94s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 47 ( 15 unt; 2 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 49 ~; 49 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( equalish(add(X0,X1),add(X1,X0))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
fof(f18,axiom,
! [X0,X1] :
( less_or_equal(X0,X1)
| less_or_equal(X1,X0)
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f22,axiom,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| less_or_equal(X0,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(f29,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f31,axiom,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_is_defined) ).
fof(f32,negated_conjecture,
equalish(add(a,a),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_u_5) ).
fof(f33,negated_conjecture,
equalish(add(b,b),v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_v_6) ).
fof(f34,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_7) ).
fof(f35,negated_conjecture,
~ less_or_equal(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_8) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( ~ less_or_equal(X1,X2)
| ~ defined(X0)
| less_or_equal(X3,add(X2,X0))
| ~ equalish(add(X1,X0),X3) ),
inference(resolution,[],[f19,f26]) ).
fof(f221,plain,
! [X0,X1] :
( ~ equalish(add(a,X0),X1)
| less_or_equal(X1,add(b,X0))
| ~ defined(X0) ),
inference(resolution,[],[f104,f34]) ).
fof(f287,plain,
! [X0] :
( less_or_equal(add(X0,a),add(b,X0))
| ~ defined(X0)
| ~ defined(a)
| ~ defined(X0) ),
inference(resolution,[],[f221,f4]) ).
fof(f292,plain,
( less_or_equal(u,add(b,a))
| ~ defined(a) ),
inference(resolution,[],[f221,f32]) ).
fof(f298,plain,
! [X0] :
( less_or_equal(add(X0,a),add(b,X0))
| ~ defined(X0)
| ~ defined(a) ),
inference(duplicate_literal_removal,[],[f287]) ).
fof(f299,plain,
less_or_equal(u,add(b,a)),
inference(forward_subsumption_resolution,[],[f292,f28]) ).
fof(f302,plain,
! [X0] :
( less_or_equal(add(X0,a),add(b,X0))
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[],[f298,f28]) ).
fof(f309,plain,
! [X0] :
( ~ less_or_equal(add(b,a),X0)
| less_or_equal(u,X0) ),
inference(resolution,[],[f299,f17]) ).
fof(f343,definition,
( spl0_23
<=> less_or_equal(add(b,a),v) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f344,plain,
( less_or_equal(add(b,a),v)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f473,definition,
( spl0_30
<=> less_or_equal(v,v) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f474,plain,
( less_or_equal(v,v)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f475,plain,
( ~ less_or_equal(v,v)
| spl0_30 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f486,plain,
( less_or_equal(v,v)
| ~ defined(v)
| ~ defined(v)
| spl0_30 ),
inference(resolution,[],[f475,f18]) ).
fof(f487,plain,
( less_or_equal(v,v)
| ~ defined(v)
| spl0_30 ),
inference(duplicate_literal_removal,[],[f486]) ).
fof(f488,plain,
( ~ defined(v)
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f487,f475]) ).
fof(f489,plain,
( $false
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f488,f31]) ).
fof(f490,plain,
spl0_30,
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f498,plain,
( ! [X0] :
( ~ equalish(v,X0)
| less_or_equal(X0,v) )
| ~ spl0_30 ),
inference(resolution,[],[f474,f26]) ).
fof(f641,plain,
( ! [X0] :
( ~ equalish(X0,v)
| less_or_equal(X0,v) )
| ~ spl0_30 ),
inference(resolution,[],[f498,f22]) ).
fof(f744,plain,
! [X0,X1] :
( ~ less_or_equal(add(b,X0),X1)
| less_or_equal(add(X0,a),X1)
| ~ defined(X0) ),
inference(resolution,[],[f302,f17]) ).
fof(f877,plain,
( less_or_equal(add(b,b),v)
| ~ spl0_30 ),
inference(resolution,[],[f641,f33]) ).
fof(f5577,plain,
( less_or_equal(add(b,a),v)
| ~ defined(b)
| ~ spl0_30 ),
inference(resolution,[],[f744,f877]) ).
fof(f5601,plain,
( less_or_equal(add(b,a),v)
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f5577,f29]) ).
fof(f5603,plain,
( spl0_23
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f5601,f473,f343]) ).
fof(f5635,plain,
( less_or_equal(u,v)
| ~ spl0_23 ),
inference(resolution,[],[f344,f309]) ).
fof(f5648,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f5635,f35]) ).
fof(f5649,plain,
~ spl0_23,
inference(avatar_contradiction_clause,[],[f5648]) ).
cnf(s21,plain,
spl0_30,
inference(sat_conversion,[],[f490]) ).
cnf(s316,plain,
( spl0_23
| ~ spl0_30 ),
inference(sat_conversion,[],[f5603]) ).
cnf(s324,plain,
~ spl0_23,
inference(sat_conversion,[],[f5649]) ).
cnf(s328,plain,
~ spl0_30,
inference(rat,[],[s316,s324]) ).
cnf(s352,plain,
$false,
inference(rat,[],[s21,s328]) ).
fof(f5652,plain,
$false,
inference(avatar_sat_refutation,[],[s352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD060-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n001.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 00:53:17 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 2.84/0.94 % (912959)Input is clausal, will run a generic CNF schedule.
% 2.84/0.94 % (913005)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3585480318:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 2.84/0.94 % (913000)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=3433765516:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 2.84/0.94 % (913001)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1983750120:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 2.84/0.94 % (913003)lrs+10_1_sil=8000:sp=occurrence:random_seed=190003312:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 2.84/0.94 % (913004)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1219487487:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 2.84/0.94 % (913006)dis-21_1_sil=8000:lcm=predicate:random_seed=2660074623:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 2.84/0.94 % (913002)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=8978860:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 2.84/0.94 % (913005)First to succeed.
% 2.84/0.94 % (913005)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-912959"
% 2.84/0.94 % (913006)Instruction limit reached!
% 2.84/0.94 % (913006)------------------------------
% 2.84/0.94 % (913006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/0.94 % (913006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/0.94 % (913006)CaDiCaL version: 2.1.3
% 2.84/0.94 % (913006)Termination reason: Instruction limit
% 2.84/0.94 % (913006)Termination phase: Saturation
% 2.84/0.94 % (913006)Time elapsed: 0.065 s
% 2.84/0.94 % (913006)Peak memory usage: 89 MB
% 2.84/0.94 % (913006)Instructions burned: 118 (million)
% 2.84/0.94 % (913004)Instruction limit reached!
% 2.84/0.94 % (913004)------------------------------
% 2.84/0.94 % (913004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/0.94 % (913004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/0.94 % (913004)CaDiCaL version: 2.1.3
% 2.84/0.94 % (913004)Termination reason: Instruction limit
% 2.84/0.94 % (913004)Termination phase: Saturation
% 2.84/0.94 % (913004)Time elapsed: 0.066 s
% 2.84/0.94 % (913004)Peak memory usage: 88 MB
% 2.84/0.94 % (913004)Instructions burned: 115 (million)
% 2.84/0.94 % (913003)Instruction limit reached!
% 2.84/0.94 % (913003)------------------------------
% 2.84/0.94 % (913003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/0.94 % (913003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/0.94 % (913003)CaDiCaL version: 2.1.3
% 2.84/0.94 % (913003)Termination reason: Instruction limit
% 2.84/0.94 % (913003)Termination phase: Saturation
% 2.84/0.94 % (913003)Time elapsed: 0.068 s
% 2.84/0.94 % (913003)Peak memory usage: 89 MB
% 2.84/0.94 % (913003)Instructions burned: 109 (million)
% 2.84/0.94 % (913062)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2883988049:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 2.84/0.94 % (913063)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4062323366:st=4:i=219:sd=3:ss=axioms_2998 on theBenchmark for (2998ds/219Mi)
% 2.84/0.94 % (913061)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=4050301475:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.84/0.94 % (913005)Refutation found. Thanks to Tanya!
% 2.84/0.94 % SZS status Unsatisfiable for theBenchmark
% 2.84/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 2.84/0.94 % (913005)------------------------------
% 2.84/0.94 % (913005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/0.94 % (913005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/0.94 % (913005)CaDiCaL version: 2.1.3
% 2.84/0.94 % (913005)Termination reason: Refutation
% 2.84/0.94 % (913005)Time elapsed: 0.064 s
% 2.84/0.94 % (913005)Peak memory usage: 91 MB
% 2.84/0.94 % (913005)Instructions burned: 178 (million)
% 2.84/0.94 % (913005)------------------------------
% 2.84/0.94 % (913005)------------------------------
% 2.84/0.94 % (912959)Success in time 0.339 s
% 2.84/0.94 % Vampire exiting
%------------------------------------------------------------------------------