%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD005-3 : 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 : n010.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 3.43s 1.16s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 28 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_1) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f19,axiom,
! [X0,X1] :
( sum(X0,X1,add(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
! [X0] : ~ sum(a,X0,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ sum(a,X0,X1)
| ~ sum(X0,X2,X3)
| ~ sum(X1,X2,b) ),
inference(resolution,[],[f1,f29]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ sum(X3,X1,b)
| ~ sum(X0,X1,X2)
| ~ sum(X0,a,X3) ),
inference(resolution,[],[f34,f5]) ).
fof(f103,plain,
! [X0,X1] :
( ~ sum(X0,b,X1)
| ~ sum(X0,a,additive_identity)
| ~ defined(b) ),
inference(resolution,[],[f38,f3]) ).
fof(f109,plain,
! [X0,X1] :
( ~ sum(X0,a,additive_identity)
| ~ sum(X0,b,X1) ),
inference(forward_subsumption_resolution,[],[f103,f28]) ).
fof(f116,plain,
! [X0] :
( ~ sum(additive_inverse(a),b,X0)
| ~ defined(a) ),
inference(resolution,[],[f109,f4]) ).
fof(f120,plain,
! [X0] : ~ sum(additive_inverse(a),b,X0),
inference(forward_subsumption_resolution,[],[f116,f27]) ).
fof(f129,plain,
( ~ defined(additive_inverse(a))
| ~ defined(b) ),
inference(resolution,[],[f120,f19]) ).
fof(f130,plain,
~ defined(additive_inverse(a)),
inference(forward_subsumption_resolution,[],[f129,f28]) ).
fof(f137,plain,
~ defined(a),
inference(resolution,[],[f130,f15]) ).
fof(f138,plain,
$false,
inference(forward_subsumption_resolution,[],[f137,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD005-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n010.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 00:22:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.43/1.16 % (2509787)Input is clausal, will run a generic CNF schedule.
% 3.43/1.16 % (2509794)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3098766196:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.43/1.16 % (2509797)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1591372058:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.43/1.16 % (2509795)lrs+10_1_sil=8000:sp=occurrence:random_seed=442960167:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.43/1.16 % (2509793)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4287845407:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.43/1.16 % (2509796)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2911601343:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.43/1.16 % (2509798)dis-21_1_sil=8000:lcm=predicate:random_seed=3428588558: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)
% 3.43/1.16 % (2509792)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=1579261468:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.43/1.16 % (2509795)Refutation not found, incomplete strategy
% 3.43/1.16 % (2509795)------------------------------
% 3.43/1.16 % (2509795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.16 % (2509795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.16 % (2509795)CaDiCaL version: 2.1.3
% 3.43/1.16 % (2509795)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.16 % (2509795)Time elapsed: 0.001 s
% 3.43/1.16 % (2509795)Peak memory usage: 87 MB
% 3.43/1.16 % (2509797)First to succeed.
% 3.43/1.16 % (2509797)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2509787"
% 3.43/1.16 % (2509796)Instruction limit reached!
% 3.43/1.16 % (2509796)------------------------------
% 3.43/1.16 % (2509796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.16 % (2509796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.16 % (2509796)CaDiCaL version: 2.1.3
% 3.43/1.16 % (2509796)Termination reason: Instruction limit
% 3.43/1.16 % (2509796)Termination phase: Saturation
% 3.43/1.16 % (2509796)Time elapsed: 0.061 s
% 3.43/1.16 % (2509796)Peak memory usage: 88 MB
% 3.43/1.16 % (2509796)Instructions burned: 114 (million)
% 3.43/1.16 % (2509798)Instruction limit reached!
% 3.43/1.16 % (2509798)------------------------------
% 3.43/1.16 % (2509798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.16 % (2509798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.16 % (2509798)CaDiCaL version: 2.1.3
% 3.43/1.16 % (2509798)Termination reason: Instruction limit
% 3.43/1.16 % (2509798)Termination phase: Saturation
% 3.43/1.16 % (2509798)Time elapsed: 0.075 s
% 3.43/1.16 % (2509798)Peak memory usage: 89 MB
% 3.43/1.16 % (2509798)Instructions burned: 118 (million)
% 3.43/1.16 % (2509806)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=274027554:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.43/1.16 % (2509807)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3742742953: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)
% 3.43/1.16 % (2509806)Refutation not found, incomplete strategy
% 3.43/1.16 % (2509806)------------------------------
% 3.43/1.16 % (2509806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.16 % (2509806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.16 % (2509806)CaDiCaL version: 2.1.3
% 3.43/1.16 % (2509806)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.16 % (2509806)Time elapsed: 0.001 s
% 3.43/1.16 % (2509806)Peak memory usage: 87 MB
% 3.43/1.16 % (2509795)------------------------------
% 3.43/1.16 % (2509795)------------------------------
% 3.43/1.16 % (2509797)Refutation found. Thanks to Tanya!
% 3.43/1.16 % SZS status Unsatisfiable for theBenchmark
% 3.43/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.16 % (2509797)------------------------------
% 3.43/1.16 % (2509797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.16 % (2509797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.16 % (2509797)CaDiCaL version: 2.1.3
% 3.43/1.16 % (2509797)Termination reason: Refutation
% 3.43/1.16 % (2509797)Time elapsed: 0.006 s
% 3.43/1.16 % (2509797)Peak memory usage: 88 MB
% 3.43/1.16 % (2509797)Instructions burned: 7 (million)
% 3.43/1.16 % (2509797)------------------------------
% 3.43/1.16 % (2509797)------------------------------
% 3.43/1.16 % (2509787)Success in time 0.408 s
% 3.43/1.16 % Vampire exiting
%------------------------------------------------------------------------------