%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD069-3 : 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 : n009.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 2.76s 1.17s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f21,axiom,
! [X0,X1] :
( sum(additive_identity,X0,X1)
| ~ less_or_equal(X0,X1)
| ~ less_or_equal(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X4] :
( ~ sum(X3,X4,X1)
| ~ less_or_equal(X2,X3)
| ~ sum(X2,X4,X0)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f30,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f31,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
fof(f32,negated_conjecture,
sum(a,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
fof(f38,plain,
( ~ less_or_equal(b,additive_identity)
| ~ less_or_equal(additive_identity,b) ),
inference(resolution,[],[f21,f31]) ).
fof(f40,plain,
~ less_or_equal(b,additive_identity),
inference(forward_subsumption_resolution,[],[f38,f30]) ).
fof(f57,plain,
! [X0,X1] :
( ~ sum(X0,b,X1)
| ~ less_or_equal(X0,a)
| less_or_equal(X1,additive_identity) ),
inference(resolution,[],[f24,f32]) ).
fof(f68,plain,
( ~ less_or_equal(additive_identity,a)
| less_or_equal(b,additive_identity)
| ~ defined(b) ),
inference(resolution,[],[f57,f3]) ).
fof(f71,plain,
( less_or_equal(b,additive_identity)
| ~ defined(b) ),
inference(forward_subsumption_resolution,[],[f68,f29]) ).
fof(f81,plain,
~ defined(b),
inference(forward_subsumption_resolution,[],[f71,f40]) ).
fof(f82,plain,
$false,
inference(forward_subsumption_resolution,[],[f81,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD069-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 00:48:45 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 2.76/1.17 % (3666014)Input is clausal, will run a generic CNF schedule.
% 2.76/1.17 % (3666022)lrs+10_1_sil=8000:sp=occurrence:random_seed=68765587:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.76/1.17 % (3666022)First to succeed.
% 2.76/1.17 % (3666022)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3666014"
% 2.76/1.17 % (3666021)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3249522077:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.76/1.17 % (3666020)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2926951260:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.76/1.17 % (3666019)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=1212404479:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.76/1.17 % (3666024)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2103094169:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.76/1.17 % (3666023)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3637707977:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.76/1.17 % (3666025)dis-21_1_sil=8000:lcm=predicate:random_seed=1783950626: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)
% 2.76/1.17 % (3666023)Also succeeded, but the first one will report.
% 2.76/1.17 % (3666024)Also succeeded, but the first one will report.
% 2.76/1.17 % (3666025)Also succeeded, but the first one will report.
% 2.76/1.17 % (3666022)Refutation found. Thanks to Tanya!
% 2.76/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.76/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.17 % (3666022)------------------------------
% 2.76/1.17 % (3666022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.17 % (3666022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.17 % (3666022)CaDiCaL version: 2.1.3
% 2.76/1.17 % (3666022)Termination reason: Refutation
% 2.76/1.17 % (3666022)Time elapsed: 0.002 s
% 2.76/1.17 % (3666022)Peak memory usage: 88 MB
% 2.76/1.17 % (3666022)Instructions burned: 2 (million)
% 2.76/1.17 % (3666022)------------------------------
% 2.76/1.17 % (3666022)------------------------------
% 2.76/1.17 % (3666014)Success in time 0.297 s
% 2.76/1.17 % Vampire exiting
%------------------------------------------------------------------------------