%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:11:36 PM UTC 2026
% Result : Unsatisfiable 3.51s 1.47s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : equalish(add(X0,n0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adding_zero) ).
fof(f9,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_lemma) ).
fof(f11,axiom,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
fof(f12,axiom,
! [X2,X0,X1] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f13,axiom,
! [X2,X0,X1] :
( ~ equalish(add(X0,X1),add(X2,X1))
| equalish(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_substitution) ).
fof(f14,axiom,
! [X0,X1] : equalish(add(X0,X1),add(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_plus) ).
fof(f15,axiom,
less(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impossible_a_is_less_than_itself) ).
fof(f16,negated_conjecture,
! [X0] : ~ equalish(successor(X0),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_contradiction) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X2,add(X1,X3))
| ~ equalish(add(X0,X3),X2) ),
inference(resolution,[],[f13,f12]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ equalish(add(X1,X2),add(X0,X2))
| equalish(X0,X1) ),
inference(resolution,[],[f13,f11]) ).
fof(f44,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a),
inference(resolution,[],[f9,f15]) ).
fof(f52,plain,
! [X0] : equalish(X0,add(X0,n0)),
inference(resolution,[],[f37,f1]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ equalish(add(successor(X2),X1),X0)
| ~ equalish(X0,add(n0,X1)) ),
inference(resolution,[],[f36,f16]) ).
fof(f189,plain,
~ equalish(a,add(n0,a)),
inference(resolution,[],[f80,f44]) ).
fof(f192,plain,
! [X0] :
( ~ equalish(X0,add(n0,a))
| ~ equalish(a,X0) ),
inference(resolution,[],[f189,f12]) ).
fof(f623,plain,
~ equalish(a,add(a,n0)),
inference(resolution,[],[f192,f14]) ).
fof(f643,plain,
$false,
inference(resolution,[],[f623,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 18:42:42 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.51/1.47 % (3135478)Input is clausal, will run a generic CNF schedule.
% 3.51/1.47 % (3135484)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=841947714:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.51/1.47 % (3135489)dis-21_1_sil=8000:lcm=predicate:random_seed=2390505805: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)
% 3.51/1.47 % (3135486)lrs+10_1_sil=8000:sp=occurrence:random_seed=396006274:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.51/1.47 % (3135487)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=79035925:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.51/1.47 % (3135483)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=2790207374:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.51/1.47 % (3135485)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=45957210:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.51/1.47 % (3135488)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3183168543:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.51/1.47 % (3135489)First to succeed.
% 3.51/1.47 % (3135489)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3135478"
% 3.51/1.47 % (3135488)Also succeeded, but the first one will report.
% 3.51/1.47 % (3135486)Also succeeded, but the first one will report.
% 3.51/1.47 % (3135487)Instruction limit reached!
% 3.51/1.47 % (3135487)------------------------------
% 3.51/1.47 % (3135487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.47 % (3135487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.47 % (3135487)CaDiCaL version: 2.1.3
% 3.51/1.47 % (3135487)Termination reason: Instruction limit
% 3.51/1.47 % (3135487)Termination phase: Saturation
% 3.51/1.47 % (3135487)Time elapsed: 0.071 s
% 3.51/1.47 % (3135487)Peak memory usage: 88 MB
% 3.51/1.47 % (3135487)Instructions burned: 116 (million)
% 3.51/1.47 % (3135497)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=4082569381:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.51/1.47 % (3135497)Refutation not found, incomplete strategy
% 3.51/1.47 % (3135497)------------------------------
% 3.51/1.47 % (3135497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.47 % (3135497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.47 % (3135497)CaDiCaL version: 2.1.3
% 3.51/1.47 % (3135497)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.47 % (3135497)Time elapsed: 0.001 s
% 3.51/1.47 % (3135497)Peak memory usage: 87 MB
% 3.51/1.47 % (3135489)Refutation found. Thanks to Tanya!
% 3.51/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.51/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.47 % (3135489)------------------------------
% 3.51/1.47 % (3135489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.47 % (3135489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.47 % (3135489)CaDiCaL version: 2.1.3
% 3.51/1.47 % (3135489)Termination reason: Refutation
% 3.51/1.47 % (3135489)Time elapsed: 0.011 s
% 3.51/1.47 % (3135489)Peak memory usage: 88 MB
% 3.51/1.47 % (3135489)Instructions burned: 16 (million)
% 3.51/1.47 % (3135489)------------------------------
% 3.51/1.47 % (3135489)------------------------------
% 3.51/1.47 % (3135478)Success in time 0.415 s
% 3.51/1.47 % Vampire exiting
%------------------------------------------------------------------------------