%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD013-3 : 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 09:49:00 AM UTC 2026
% Result : Unsatisfiable 5.62s 1.67s
% Output : Refutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 30 ~; 27 |; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_1) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2)
| ~ sum(X3,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
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(f30,axiom,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
fof(f31,negated_conjecture,
sum(additive_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_5) ).
fof(f32,negated_conjecture,
sum(additive_identity,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
fof(f33,negated_conjecture,
~ sum(a,c,add(d,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).
fof(f39,plain,
! [X0,X1] :
( sum(X1,X0,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[],[f19,f5]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ sum(X1,X2,X3)
| ~ sum(X0,X1,additive_identity)
| sum(X0,X3,X2)
| ~ defined(X2) ),
inference(resolution,[],[f1,f3]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ sum(X0,d,X2)
| sum(X1,c,X2)
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[],[f2,f32]) ).
fof(f92,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ defined(d)
| sum(X1,c,add(d,X0))
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[],[f39,f56]) ).
fof(f93,plain,
! [X0,X1] :
( sum(X1,c,add(d,X0))
| ~ defined(X0)
| ~ sum(X0,additive_identity,X1) ),
inference(forward_subsumption_resolution,[],[f92,f30]) ).
fof(f105,plain,
! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,b,a)
| ~ defined(a) ),
inference(resolution,[],[f45,f31]) ).
fof(f117,plain,
! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,b,a) ),
inference(forward_subsumption_resolution,[],[f105,f27]) ).
fof(f217,plain,
( sum(additive_identity,b,a)
| ~ defined(additive_identity) ),
inference(resolution,[],[f117,f3]) ).
fof(f218,plain,
sum(additive_identity,b,a),
inference(forward_subsumption_resolution,[],[f217,f14]) ).
fof(f225,plain,
sum(b,additive_identity,a),
inference(resolution,[],[f218,f5]) ).
fof(f481,plain,
( ~ defined(b)
| ~ sum(b,additive_identity,a) ),
inference(resolution,[],[f93,f33]) ).
fof(f486,plain,
~ sum(b,additive_identity,a),
inference(forward_subsumption_resolution,[],[f481,f28]) ).
fof(f489,plain,
$false,
inference(forward_subsumption_resolution,[],[f486,f225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD013-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n010.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 00:25:33 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.29 Running first-order theorem proving
% 0.26/0.29 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
% 5.62/1.67 % (2512420)Input is clausal, will run a generic CNF schedule.
% 5.62/1.67 % (2512426)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3022667902:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.62/1.67 % (2512430)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=964391183:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.62/1.67 % (2512427)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=904685532:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.62/1.67 % (2512431)dis-21_1_sil=8000:lcm=predicate:random_seed=642390655: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)
% 5.62/1.67 % (2512425)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=980964425:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.62/1.67 % (2512428)lrs+10_1_sil=8000:sp=occurrence:random_seed=3297551069:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.62/1.67 % (2512428)First to succeed.
% 5.62/1.67 % (2512428)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2512420"
% 5.62/1.67 % (2512429)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=640694159:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.62/1.67 % (2512430)Instruction limit reached!
% 5.62/1.67 % (2512430)------------------------------
% 5.62/1.67 % (2512430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.67 % (2512430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.67 % (2512430)CaDiCaL version: 2.1.3
% 5.62/1.67 % (2512430)Termination reason: Instruction limit
% 5.62/1.67 % (2512430)Termination phase: Saturation
% 5.62/1.67 % (2512430)Time elapsed: 0.144 s
% 5.62/1.67 % (2512430)Peak memory usage: 89 MB
% 5.62/1.67 % (2512430)Instructions burned: 180 (million)
% 5.62/1.67 % (2512431)Instruction limit reached!
% 5.62/1.67 % (2512431)------------------------------
% 5.62/1.67 % (2512431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.67 % (2512431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.67 % (2512431)CaDiCaL version: 2.1.3
% 5.62/1.67 % (2512431)Termination reason: Instruction limit
% 5.62/1.67 % (2512431)Termination phase: Saturation
% 5.62/1.67 % (2512431)Time elapsed: 0.116 s
% 5.62/1.67 % (2512431)Peak memory usage: 89 MB
% 5.62/1.67 % (2512431)Instructions burned: 117 (million)
% 5.62/1.67 % (2512429)Instruction limit reached!
% 5.62/1.67 % (2512429)------------------------------
% 5.62/1.67 % (2512429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.67 % (2512429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.67 % (2512429)CaDiCaL version: 2.1.3
% 5.62/1.67 % (2512429)Termination reason: Instruction limit
% 5.62/1.67 % (2512429)Termination phase: Saturation
% 5.62/1.67 % (2512429)Time elapsed: 0.115 s
% 5.62/1.67 % (2512429)Peak memory usage: 88 MB
% 5.62/1.67 % (2512429)Instructions burned: 115 (million)
% 5.62/1.67 % (2512441)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=59847310:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 5.62/1.67 % (2512443)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3887782503:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 5.62/1.67 % (2512442)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4171011518:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 5.62/1.67 % (2512442)Also succeeded, but the first one will report.
% 5.62/1.67 % (2512428)Refutation found. Thanks to Tanya!
% 5.62/1.67 % SZS status Unsatisfiable for theBenchmark
% 5.62/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 5.62/1.67 % (2512428)------------------------------
% 5.62/1.67 % (2512428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.67 % (2512428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.67 % (2512428)CaDiCaL version: 2.1.3
% 5.62/1.67 % (2512428)Termination reason: Refutation
% 5.62/1.67 % (2512428)Time elapsed: 0.018 s
% 5.62/1.67 % (2512428)Peak memory usage: 88 MB
% 5.62/1.67 % (2512428)Instructions burned: 16 (million)
% 5.62/1.67 % (2512428)------------------------------
% 5.62/1.67 % (2512428)------------------------------
% 5.62/1.67 % (2512420)Success in time 0.684 s
% 5.62/1.67 % Vampire exiting
%------------------------------------------------------------------------------