%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD016-5 : 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 : n012.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 09:49:01 AM UTC 2026
% Result : Unsatisfiable 4.54s 1.03s
% Output : Refutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 17 ( 17 !; 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
fof(f29,axiom,
defined(v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_is_defined) ).
fof(f32,negated_conjecture,
sum(a,u,q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).
fof(f33,negated_conjecture,
sum(a,v,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_7) ).
fof(f34,negated_conjecture,
sum(additive_identity,q,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_8) ).
fof(f35,negated_conjecture,
~ sum(additive_identity,u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_9) ).
fof(f37,plain,
sum(u,a,q),
inference(unit_resulting_resolution,[],[f5,f32]) ).
fof(f43,plain,
sum(additive_identity,v,v),
inference(unit_resulting_resolution,[],[f3,f29]) ).
fof(f54,plain,
sum(additive_identity,u,u),
inference(unit_resulting_resolution,[],[f3,f28]) ).
fof(f56,plain,
sum(u,a,r),
inference(unit_resulting_resolution,[],[f2,f34,f37,f54]) ).
fof(f63,plain,
sum(a,u,r),
inference(unit_resulting_resolution,[],[f5,f56]) ).
fof(f101,plain,
sum(additive_inverse(a),a,additive_identity),
inference(unit_resulting_resolution,[],[f4,f27]) ).
fof(f109,plain,
sum(additive_inverse(a),r,v),
inference(unit_resulting_resolution,[],[f1,f43,f33,f101]) ).
fof(f113,plain,
~ sum(additive_inverse(a),r,v),
inference(unit_resulting_resolution,[],[f2,f63,f35,f101]) ).
fof(f115,plain,
$false,
inference(forward_subsumption_resolution,[],[f113,f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD016-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 00:27:19 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 3.70/0.94 % (3948697)Input is clausal, will run a generic CNF schedule.
% 3.70/0.94 % (3948710)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3730347339:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.70/0.94 % (3948709)lrs+10_1_sil=8000:sp=occurrence:random_seed=2377006944:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.70/0.94 % (3948706)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=2365295462:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.70/0.94 % (3948708)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2401909002:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.70/0.94 % (3948707)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3398432040:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.70/0.94 % (3948711)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1626150737:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.70/0.94 % (3948709)Refutation not found, incomplete strategy
% 3.70/0.94 % (3948709)------------------------------
% 3.70/0.94 % (3948709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/0.94 % (3948709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (3948709)CaDiCaL version: 2.1.3
% 3.70/0.94 % (3948709)Termination reason: Refutation not found, incomplete strategy
% 3.70/0.94 % (3948709)Time elapsed: 0.004 s
% 3.70/0.94 % (3948709)Peak memory usage: 87 MB
% 3.70/0.94 % (3948709)Instructions burned: 11 (million)
% 3.70/0.94 % (3948712)dis-21_1_sil=8000:lcm=predicate:random_seed=4207847324: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)
% 3.70/0.94 % (3948710)Instruction limit reached!
% 3.70/0.94 % (3948710)------------------------------
% 3.70/0.94 % (3948710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/0.94 % (3948710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (3948710)CaDiCaL version: 2.1.3
% 3.70/0.94 % (3948710)Termination reason: Instruction limit
% 3.70/0.94 % (3948710)Termination phase: Saturation
% 3.70/0.94 % (3948710)Time elapsed: 0.035 s
% 3.70/0.94 % (3948710)Peak memory usage: 88 MB
% 3.70/0.94 % (3948710)Instructions burned: 116 (million)
% 3.70/0.94 % (3948712)Instruction limit reached!
% 3.70/0.94 % (3948712)------------------------------
% 3.70/0.94 % (3948712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/0.94 % (3948712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (3948712)CaDiCaL version: 2.1.3
% 3.70/0.94 % (3948712)Termination reason: Instruction limit
% 3.70/0.94 % (3948712)Termination phase: Saturation
% 3.70/0.94 % (3948712)Time elapsed: 0.040 s
% 3.70/0.94 % (3948712)Peak memory usage: 89 MB
% 3.70/0.94 % (3948712)Instructions burned: 119 (million)
% 3.70/0.94 % (3948711)Instruction limit reached!
% 3.70/0.94 % (3948711)------------------------------
% 3.70/0.94 % (3948711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/0.94 % (3948711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/0.94 % (3948711)CaDiCaL version: 2.1.3
% 3.70/0.94 % (3948711)Termination reason: Instruction limit
% 3.70/0.94 % (3948711)Termination phase: Saturation
% 3.70/0.94 % (3948711)Time elapsed: 0.057 s
% 3.70/0.94 % (3948711)Peak memory usage: 88 MB
% 3.70/0.94 % (3948711)Instructions burned: 180 (million)
% 3.70/0.94 % (3948720)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=3335509379:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.70/0.94 % (3948721)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=286351689:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 3.70/0.94 % (3948722)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=465427448:st=4:i=219:sd=3:ss=axioms_2998 on theBenchmark for (2998ds/219Mi)
% 3.70/0.94 % (3948709)------------------------------
% 3.70/0.94 % (3948709)------------------------------
% 3.70/0.94 % (3948720)Instruction limit reached!
% 3.70/0.94 % (3948720)------------------------------
% 4.54/1.03 % (3948720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948720)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948720)Termination reason: Instruction limit
% 4.54/1.03 % (3948720)Termination phase: Saturation
% 4.54/1.03 % (3948720)Time elapsed: 0.046 s
% 4.54/1.03 % (3948720)Peak memory usage: 89 MB
% 4.54/1.03 % (3948720)Instructions burned: 146 (million)
% 4.54/1.03 % (3948721)Instruction limit reached!
% 4.54/1.03 % (3948721)------------------------------
% 4.54/1.03 % (3948721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948721)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948721)Termination reason: Instruction limit
% 4.54/1.03 % (3948721)Termination phase: Saturation
% 4.54/1.03 % (3948721)Time elapsed: 0.051 s
% 4.54/1.03 % (3948721)Peak memory usage: 93 MB
% 4.54/1.03 % (3948721)Instructions burned: 190 (million)
% 4.54/1.03 % (3948722)Instruction limit reached!
% 4.54/1.03 % (3948722)------------------------------
% 4.54/1.03 % (3948722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948722)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948722)Termination reason: Instruction limit
% 4.54/1.03 % (3948722)Termination phase: Saturation
% 4.54/1.03 % (3948722)Time elapsed: 0.070 s
% 4.54/1.03 % (3948722)Peak memory usage: 88 MB
% 4.54/1.03 % (3948722)Instructions burned: 222 (million)
% 4.54/1.03 % (3948726)lrs+10_64_to=lpo:sil=8000:random_seed=972591078:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.54/1.03 % (3948727)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4275732936:avsq=on:i=194:fgj=on:bd=preordered_2997 on theBenchmark for (2997ds/194Mi)
% 4.54/1.03 % (3948728)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2918509537:i=157:gtg=all_2997 on theBenchmark for (2997ds/157Mi)
% 4.54/1.03 % (3948726)Instruction limit reached!
% 4.54/1.03 % (3948726)------------------------------
% 4.54/1.03 % (3948726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948726)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948726)Termination reason: Instruction limit
% 4.54/1.03 % (3948726)Termination phase: Saturation
% 4.54/1.03 % (3948726)Time elapsed: 0.040 s
% 4.54/1.03 % (3948726)Peak memory usage: 90 MB
% 4.54/1.03 % (3948726)Instructions burned: 127 (million)
% 4.54/1.03 % (3948729)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3313695832:i=3394:sd=4:ss=included:sgt=64_2996 on theBenchmark for (2996ds/3394Mi)
% 4.54/1.03 % (3948727)Instruction limit reached!
% 4.54/1.03 % (3948727)------------------------------
% 4.54/1.03 % (3948727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948727)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948727)Termination reason: Instruction limit
% 4.54/1.03 % (3948727)Termination phase: Saturation
% 4.54/1.03 % (3948727)Time elapsed: 0.070 s
% 4.54/1.03 % (3948727)Peak memory usage: 89 MB
% 4.54/1.03 % (3948727)Instructions burned: 194 (million)
% 4.54/1.03 % (3948728)Instruction limit reached!
% 4.54/1.03 % (3948728)------------------------------
% 4.54/1.03 % (3948728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948728)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948728)Termination reason: Instruction limit
% 4.54/1.03 % (3948728)Termination phase: Saturation
% 4.54/1.03 % (3948728)Time elapsed: 0.057 s
% 4.54/1.03 % (3948728)Peak memory usage: 90 MB
% 4.54/1.03 % (3948728)Instructions burned: 159 (million)
% 4.54/1.03 % (3948707)First to succeed.
% 4.54/1.03 % (3948707)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3948697"
% 4.54/1.03 % (3948706)Also succeeded, but the first one will report.
% 4.54/1.03 % (3948733)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2815868371:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2996 on theBenchmark for (2996ds/106Mi)
% 4.54/1.03 % (3948733)Instruction limit reached!
% 4.54/1.03 % (3948733)------------------------------
% 4.54/1.03 % (3948733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948733)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948733)Termination reason: Instruction limit
% 4.54/1.03 % (3948733)Termination phase: Saturation
% 4.54/1.03 % (3948733)Time elapsed: 0.031 s
% 4.54/1.03 % (3948733)Peak memory usage: 90 MB
% 4.54/1.03 % (3948733)Instructions burned: 108 (million)
% 4.54/1.03 % (3948736)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1059331885:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2995 on theBenchmark for (2995ds/242Mi)
% 4.54/1.03 % (3948735)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3015898656:i=107_2995 on theBenchmark for (2995ds/107Mi)
% 4.54/1.03 % (3948735)Instruction limit reached!
% 4.54/1.03 % (3948735)------------------------------
% 4.54/1.03 % (3948735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948735)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948735)Termination reason: Instruction limit
% 4.54/1.03 % (3948735)Termination phase: Saturation
% 4.54/1.03 % (3948735)Time elapsed: 0.032 s
% 4.54/1.03 % (3948735)Peak memory usage: 88 MB
% 4.54/1.03 % (3948735)Instructions burned: 109 (million)
% 4.54/1.03 % (3948736)Instruction limit reached!
% 4.54/1.03 % (3948736)------------------------------
% 4.54/1.03 % (3948736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.03 % (3948736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.03 % (3948736)CaDiCaL version: 2.1.3
% 4.54/1.03 % (3948736)Termination reason: Instruction limit
% 4.54/1.03 % (3948736)Termination phase: Saturation
% 4.54/1.03 % (3948736)Time elapsed: 0.082 s
% 4.54/1.03 % (3948736)Peak memory usage: 88 MB
% 4.54/1.03 % (3948736)Instructions burned: 244 (million)
% 4.54/1.03 % (3948707)Refutation found. Thanks to Tanya!
% 4.54/1.03 % SZS status Unsatisfiable for theBenchmark
% 4.54/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 4.54/1.04 % (3948707)------------------------------
% 4.54/1.04 % (3948707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.04 % (3948707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.04 % (3948707)CaDiCaL version: 2.1.3
% 4.54/1.04 % (3948707)Termination reason: Refutation
% 4.54/1.04 % (3948707)Time elapsed: 0.349 s
% 4.54/1.04 % (3948707)Peak memory usage: 125 MB
% 4.54/1.04 % (3948707)Instructions burned: 920 (million)
% 4.54/1.04 % (3948707)------------------------------
% 4.54/1.04 % (3948707)------------------------------
% 4.54/1.04 % (3948697)Success in time 0.613 s
% 4.54/1.04 % Vampire exiting
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