%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD005-1 : 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 : n020.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 09:48:57 AM UTC 2026
% Result : Unsatisfiable 4.09s 1.35s
% Output : Refutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 13 unt; 5 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 75 ~; 61 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2))
| ~ defined(X0)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition) ).
fof(f2,axiom,
! [X0] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f3,axiom,
! [X0] :
( equalish(add(X0,additive_inverse(X0)),additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f12,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f24,axiom,
! [X2,X0,X1] :
( equalish(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ equalish(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,negated_conjecture,
! [X0] : ~ equalish(add(a,X0),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_not_equal_to_b_3) ).
fof(f170,plain,
! [X0,X1] :
( ~ equalish(add(a,X0),X1)
| ~ equalish(X1,b) ),
inference(resolution,[],[f23,f30]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ equalish(X0,b)
| ~ equalish(add(a,X1),X2)
| ~ equalish(X2,X0) ),
inference(resolution,[],[f170,f23]) ).
fof(f286,definition,
( spl0_7
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f287,plain,
( ~ defined(a)
| spl0_7 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f308,definition,
( spl0_11
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f309,plain,
( ~ defined(b)
| spl0_11 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f311,plain,
( $false
| spl0_11 ),
inference(resolution,[],[f309,f29]) ).
fof(f312,plain,
spl0_11,
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f313,plain,
( $false
| spl0_7 ),
inference(resolution,[],[f287,f28]) ).
fof(f314,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f3048,plain,
! [X2,X0,X1] :
( ~ defined(a)
| ~ defined(X0)
| ~ defined(X1)
| ~ equalish(X2,b)
| ~ equalish(add(add(a,X0),X1),X2) ),
inference(resolution,[],[f1,f274]) ).
fof(f3074,definition,
( spl0_195
<=> ! [X2,X0,X1] :
( ~ defined(X0)
| ~ equalish(add(add(a,X0),X1),X2)
| ~ equalish(X2,b)
| ~ defined(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_195])],[avatar_definition]) ).
fof(f3075,plain,
( ! [X2,X0,X1] :
( ~ equalish(add(add(a,X0),X1),X2)
| ~ defined(X0)
| ~ equalish(X2,b)
| ~ defined(X1) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f3074]) ).
fof(f3076,plain,
( spl0_195
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f3048,f286,f3074]) ).
fof(f3108,plain,
( ! [X2,X0,X1] :
( ~ defined(X0)
| ~ equalish(add(X1,X2),b)
| ~ defined(X2)
| ~ defined(X2)
| ~ equalish(add(a,X0),X1) )
| ~ spl0_195 ),
inference(resolution,[],[f3075,f24]) ).
fof(f3115,plain,
( ! [X2,X0,X1] :
( ~ equalish(add(X1,X2),b)
| ~ equalish(add(a,X0),X1)
| ~ defined(X2)
| ~ defined(X0) )
| ~ spl0_195 ),
inference(duplicate_literal_removal,[],[f3108]) ).
fof(f3170,plain,
( ! [X0] :
( ~ equalish(add(additive_identity,X0),b)
| ~ defined(X0)
| ~ defined(additive_inverse(a))
| ~ defined(a) )
| ~ spl0_195 ),
inference(resolution,[],[f3115,f3]) ).
fof(f3190,definition,
( spl0_201
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_201])],[avatar_definition]) ).
fof(f3191,plain,
( ~ defined(additive_inverse(a))
| spl0_201 ),
inference(avatar_component_clause,[],[f3190]) ).
fof(f3193,definition,
( spl0_202
<=> ! [X0] :
( ~ equalish(add(additive_identity,X0),b)
| ~ defined(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_202])],[avatar_definition]) ).
fof(f3194,plain,
( ! [X0] :
( ~ equalish(add(additive_identity,X0),b)
| ~ defined(X0) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f3193]) ).
fof(f3195,plain,
( ~ spl0_7
| ~ spl0_201
| spl0_202
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f3170,f3074,f3193,f3190,f286]) ).
fof(f3196,plain,
( ~ defined(a)
| spl0_201 ),
inference(resolution,[],[f3191,f12]) ).
fof(f3197,plain,
( ~ spl0_7
| spl0_201 ),
inference(avatar_split_clause,[],[f3196,f3190,f286]) ).
fof(f3276,plain,
( ~ defined(b)
| ~ defined(b)
| ~ spl0_202 ),
inference(resolution,[],[f3194,f2]) ).
fof(f3280,plain,
( ~ defined(b)
| ~ spl0_202 ),
inference(duplicate_literal_removal,[],[f3276]) ).
fof(f3281,plain,
( ~ spl0_11
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f3280,f3193,f308]) ).
cnf(s10,plain,
spl0_11,
inference(sat_conversion,[],[f312]) ).
cnf(s11,plain,
spl0_7,
inference(sat_conversion,[],[f314]) ).
cnf(s449,plain,
( ~ spl0_7
| spl0_195 ),
inference(sat_conversion,[],[f3076]) ).
cnf(s468,plain,
( ~ spl0_7
| ~ spl0_195
| ~ spl0_201
| spl0_202 ),
inference(sat_conversion,[],[f3195]) ).
cnf(s469,plain,
( ~ spl0_7
| spl0_201 ),
inference(sat_conversion,[],[f3197]) ).
cnf(s475,plain,
( ~ spl0_11
| ~ spl0_202 ),
inference(sat_conversion,[],[f3281]) ).
cnf(s481,plain,
spl0_201,
inference(rat,[],[s469,s11]) ).
cnf(s482,plain,
spl0_195,
inference(rat,[],[s449,s11]) ).
cnf(s488,plain,
spl0_202,
inference(rat,[],[s468,s11,s481,s482]) ).
cnf(s496,plain,
~ spl0_11,
inference(rat,[],[s475,s488]) ).
cnf(s497,plain,
$false,
inference(rat,[],[s10,s496]) ).
fof(f3282,plain,
$false,
inference(avatar_sat_refutation,[],[s497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD005-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:23:05 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 4.09/1.35 % (729525)Input is clausal, will run a generic CNF schedule.
% 4.09/1.35 % (729533)lrs+10_1_sil=8000:sp=occurrence:random_seed=3132667735:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.09/1.35 % (729533)Instruction limit reached!
% 4.09/1.35 % (729533)------------------------------
% 4.09/1.35 % (729533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.35 % (729533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.35 % (729533)CaDiCaL version: 2.1.3
% 4.09/1.35 % (729533)Termination reason: Instruction limit
% 4.09/1.35 % (729533)Termination phase: Saturation
% 4.09/1.35 % (729533)Time elapsed: 0.032 s
% 4.09/1.35 % (729533)Peak memory usage: 88 MB
% 4.09/1.35 % (729533)Instructions burned: 109 (million)
% 4.09/1.35 % (729531)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=903555685:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.09/1.35 % (729530)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=1021670776:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.09/1.35 % (729532)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=644688400:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.09/1.35 % (729536)dis-21_1_sil=8000:lcm=predicate:random_seed=3631783286: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)
% 4.09/1.35 % (729534)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1072102898:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.09/1.35 % (729535)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3986948917:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.09/1.35 % (729536)First to succeed.
% 4.09/1.35 % (729536)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-729525"
% 4.09/1.35 % (729534)Instruction limit reached!
% 4.09/1.35 % (729534)------------------------------
% 4.09/1.35 % (729534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.35 % (729534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.35 % (729534)CaDiCaL version: 2.1.3
% 4.09/1.35 % (729534)Termination reason: Instruction limit
% 4.09/1.35 % (729534)Termination phase: Saturation
% 4.09/1.35 % (729534)Time elapsed: 0.070 s
% 4.09/1.35 % (729534)Peak memory usage: 88 MB
% 4.09/1.35 % (729534)Instructions burned: 114 (million)
% 4.09/1.35 % (729541)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=1210690601:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.09/1.35 % (729541)Refutation not found, incomplete strategy
% 4.09/1.35 % (729541)------------------------------
% 4.09/1.35 % (729541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.35 % (729541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.35 % (729541)CaDiCaL version: 2.1.3
% 4.09/1.35 % (729541)Termination reason: Refutation not found, incomplete strategy
% 4.09/1.35 % (729541)Time elapsed: 0.001 s
% 4.09/1.35 % (729541)Peak memory usage: 87 MB
% 4.09/1.35 % (729535)Instruction limit reached!
% 4.09/1.35 % (729535)------------------------------
% 4.09/1.35 % (729535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.35 % (729535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.35 % (729535)CaDiCaL version: 2.1.3
% 4.09/1.35 % (729535)Termination reason: Instruction limit
% 4.09/1.35 % (729535)Termination phase: Saturation
% 4.09/1.35 % (729535)Time elapsed: 0.116 s
% 4.09/1.35 % (729535)Peak memory usage: 89 MB
% 4.09/1.35 % (729535)Instructions burned: 181 (million)
% 4.09/1.35 % (729545)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1528649701: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)
% 4.09/1.35 % (729541)------------------------------
% 4.09/1.35 % (729541)------------------------------
% 4.09/1.35 % (729547)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3162141145:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.09/1.35 % (729547)Also succeeded, but the first one will report.
% 4.09/1.35 % (729536)Refutation found. Thanks to Tanya!
% 4.09/1.35 % SZS status Unsatisfiable for theBenchmark
% 4.09/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.09/1.35 % (729536)------------------------------
% 4.09/1.35 % (729536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.35 % (729536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.35 % (729536)CaDiCaL version: 2.1.3
% 4.09/1.35 % (729536)Termination reason: Refutation
% 4.09/1.35 % (729536)Time elapsed: 0.059 s
% 4.09/1.35 % (729536)Peak memory usage: 90 MB
% 4.09/1.35 % (729536)Instructions burned: 102 (million)
% 4.09/1.35 % (729536)------------------------------
% 4.09/1.35 % (729536)------------------------------
% 4.09/1.35 % (729525)Success in time 0.489 s
% 4.09/1.35 % Vampire exiting
%------------------------------------------------------------------------------