%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD043-3 : 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 : n008.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 09:49:10 AM UTC 2026
% Result : Unsatisfiable 6.89s 1.72s
% Output : Refutation 6.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2)
| ~ product(X3,X6,X0)
| ~ product(X4,X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
product(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_3) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
fof(f36,plain,
sum(additive_identity,a,a),
inference(unit_resulting_resolution,[],[f3,f27]) ).
fof(f37,plain,
sum(a,additive_identity,a),
inference(unit_resulting_resolution,[],[f5,f36]) ).
fof(f39,plain,
sum(additive_inverse(b),b,additive_identity),
inference(unit_resulting_resolution,[],[f4,f28]) ).
fof(f40,plain,
sum(additive_inverse(a),a,additive_identity),
inference(unit_resulting_resolution,[],[f4,f27]) ).
fof(f44,plain,
~ sum(b,b,b),
inference(unit_resulting_resolution,[],[f2,f30,f39,f39]) ).
fof(f67,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f2,f40,f40,f37]) ).
fof(f151,plain,
sum(b,b,b),
inference(unit_resulting_resolution,[],[f11,f29,f29,f29,f67]) ).
fof(f152,plain,
$false,
inference(forward_subsumption_resolution,[],[f151,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD043-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 00:35:25 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 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
% 5.53/1.54 % (2813978)Input is clausal, will run a generic CNF schedule.
% 5.53/1.54 % (2813987)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3577727057:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.53/1.54 % (2813987)Instruction limit reached!
% 5.53/1.54 % (2813987)------------------------------
% 5.53/1.54 % (2813987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.54 % (2813987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.54 % (2813987)CaDiCaL version: 2.1.3
% 5.53/1.54 % (2813987)Termination reason: Instruction limit
% 5.53/1.54 % (2813987)Termination phase: Saturation
% 5.53/1.54 % (2813987)Time elapsed: 0.033 s
% 5.53/1.54 % (2813987)Peak memory usage: 88 MB
% 5.53/1.54 % (2813987)Instructions burned: 115 (million)
% 5.53/1.54 % (2813988)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3603485480:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.53/1.54 % (2813986)lrs+10_1_sil=8000:sp=occurrence:random_seed=1979392853:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.53/1.54 % (2813984)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3657530573:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.53/1.54 % (2813983)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=3678012841:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.53/1.54 % (2813985)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3136652293:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.53/1.54 % (2813986)Refutation not found, incomplete strategy
% 5.53/1.54 % (2813986)------------------------------
% 5.53/1.54 % (2813986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.54 % (2813986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.54 % (2813986)CaDiCaL version: 2.1.3
% 5.53/1.54 % (2813986)Termination reason: Refutation not found, incomplete strategy
% 5.53/1.54 % (2813986)Time elapsed: 0.004 s
% 5.53/1.54 % (2813986)Peak memory usage: 88 MB
% 5.53/1.54 % (2813986)Instructions burned: 4 (million)
% 5.53/1.54 % (2813989)dis-21_1_sil=8000:lcm=predicate:random_seed=4173078046: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)
% 5.53/1.54 % (2813991)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=1719412437:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.53/1.54 % (2813989)Instruction limit reached!
% 5.53/1.54 % (2813989)------------------------------
% 5.53/1.54 % (2813989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.54 % (2813989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.54 % (2813989)CaDiCaL version: 2.1.3
% 5.53/1.54 % (2813989)Termination reason: Instruction limit
% 5.53/1.54 % (2813989)Termination phase: Saturation
% 5.53/1.54 % (2813989)Time elapsed: 0.074 s
% 5.53/1.54 % (2813989)Peak memory usage: 89 MB
% 5.53/1.54 % (2813989)Instructions burned: 118 (million)
% 5.53/1.54 % (2813988)Instruction limit reached!
% 5.53/1.54 % (2813988)------------------------------
% 5.53/1.54 % (2813988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.54 % (2813988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.54 % (2813988)CaDiCaL version: 2.1.3
% 5.53/1.54 % (2813988)Termination reason: Instruction limit
% 5.53/1.54 % (2813988)Termination phase: Saturation
% 5.53/1.54 % (2813988)Time elapsed: 0.112 s
% 5.53/1.54 % (2813988)Peak memory usage: 89 MB
% 5.53/1.54 % (2813988)Instructions burned: 181 (million)
% 5.53/1.54 % (2813991)Instruction limit reached!
% 5.53/1.54 % (2813991)------------------------------
% 5.53/1.54 % (2813991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.54 % (2813991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.54 % (2813991)CaDiCaL version: 2.1.3
% 5.53/1.54 % (2813991)Termination reason: Instruction limit
% 5.53/1.54 % (2813991)Termination phase: Saturation
% 5.53/1.54 % (2813991)Time elapsed: 0.041 s
% 5.53/1.54 % (2813991)Peak memory usage: 88 MB
% 5.53/1.54 % (2813991)Instructions burned: 145 (million)
% 5.53/1.54 % (2813999)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3643951186: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)
% 6.89/1.72 % (2814001)lrs+10_64_to=lpo:sil=8000:random_seed=788652126:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 6.89/1.72 % (2814000)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2874587984:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.89/1.72 % (2813986)------------------------------
% 6.89/1.72 % (2813986)------------------------------
% 6.89/1.72 % (2814001)Instruction limit reached!
% 6.89/1.72 % (2814001)------------------------------
% 6.89/1.72 % (2814001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.72 % (2814001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.72 % (2814001)CaDiCaL version: 2.1.3
% 6.89/1.72 % (2814001)Termination reason: Instruction limit
% 6.89/1.72 % (2814001)Termination phase: Saturation
% 6.89/1.72 % (2814001)Time elapsed: 0.042 s
% 6.89/1.72 % (2814001)Peak memory usage: 89 MB
% 6.89/1.72 % (2814001)Instructions burned: 128 (million)
% 6.89/1.72 % (2813999)Instruction limit reached!
% 6.89/1.72 % (2813999)------------------------------
% 6.89/1.72 % (2813999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.72 % (2813999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.72 % (2813999)CaDiCaL version: 2.1.3
% 6.89/1.72 % (2813999)Termination reason: Instruction limit
% 6.89/1.72 % (2813999)Termination phase: Saturation
% 6.89/1.72 % (2813999)Time elapsed: 0.097 s
% 6.89/1.72 % (2813999)Peak memory usage: 93 MB
% 6.89/1.72 % (2813999)Instructions burned: 190 (million)
% 6.89/1.72 % (2814006)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2800159167:i=157:gtg=all_2996 on theBenchmark for (2996ds/157Mi)
% 6.89/1.72 % (2814000)Instruction limit reached!
% 6.89/1.72 % (2814000)------------------------------
% 6.89/1.72 % (2814000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.72 % (2814000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.72 % (2814000)CaDiCaL version: 2.1.3
% 6.89/1.72 % (2814000)Termination reason: Instruction limit
% 6.89/1.72 % (2814000)Termination phase: Saturation
% 6.89/1.72 % (2814000)Time elapsed: 0.129 s
% 6.89/1.72 % (2814000)Peak memory usage: 88 MB
% 6.89/1.72 % (2814000)Instructions burned: 219 (million)
% 6.89/1.72 % (2814005)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3123015477:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 6.89/1.72 % (2814006)Instruction limit reached!
% 6.89/1.72 % (2814006)------------------------------
% 6.89/1.72 % (2814006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.72 % (2814006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.72 % (2814006)CaDiCaL version: 2.1.3
% 6.89/1.72 % (2814006)Termination reason: Instruction limit
% 6.89/1.72 % (2814006)Termination phase: Saturation
% 6.89/1.72 % (2814006)Time elapsed: 0.056 s
% 6.89/1.72 % (2814006)Peak memory usage: 90 MB
% 6.89/1.72 % (2814006)Instructions burned: 158 (million)
% 6.89/1.72 % (2814007)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1706253161:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 6.89/1.72 % (2814011)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2571803795:i=107_2994 on theBenchmark for (2994ds/107Mi)
% 6.89/1.72 % (2814009)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=884876324:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 6.89/1.72 % (2814011)Instruction limit reached!
% 6.89/1.72 % (2814011)------------------------------
% 6.89/1.72 % (2814011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.72 % (2814011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.72 % (2814011)CaDiCaL version: 2.1.3
% 6.89/1.72 % (2814011)Termination reason: Instruction limit
% 6.89/1.72 % (2814011)Termination phase: Saturation
% 6.89/1.72 % (2814011)Time elapsed: 0.037 s
% 6.89/1.72 % (2814011)Peak memory usage: 88 MB
% 6.89/1.72 % (2814011)Instructions burned: 108 (million)
% 6.89/1.72 % (2814005)Instruction limit reached!
% 6.89/1.72 % (2814005)------------------------------
% 6.89/1.72 % (2814005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.72 % (2814005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.72 % (2814005)CaDiCaL version: 2.1.3
% 6.89/1.72 % (2814005)Termination reason: Instruction limit
% 6.89/1.72 % (2814005)Termination phase: Saturation
% 6.89/1.72 % (2814005)Time elapsed: 0.140 s
% 6.89/1.72 % (2814005)Peak memory usage: 89 MB
% 6.89/1.72 % (2814005)Instructions burned: 195 (million)
% 6.89/1.72 % (2814009)Instruction limit reached!
% 6.89/1.72 % (2814009)------------------------------
% 6.89/1.72 % (2814009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.72 % (2814009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.72 % (2814009)CaDiCaL version: 2.1.3
% 6.89/1.72 % (2814009)Termination reason: Instruction limit
% 6.89/1.72 % (2814009)Termination phase: Saturation
% 6.89/1.72 % (2814009)Time elapsed: 0.055 s
% 6.89/1.72 % (2814009)Peak memory usage: 90 MB
% 6.89/1.72 % (2814009)Instructions burned: 106 (million)
% 6.89/1.72 % (2813984)First to succeed.
% 6.89/1.72 % (2813984)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2813978"
% 6.89/1.72 % (2814016)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=47456136:cond=fast:i=5208:av=off_2993 on theBenchmark for (2993ds/5208Mi)
% 6.89/1.72 % (2814015)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=158331547:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2993 on theBenchmark for (2993ds/242Mi)
% 6.89/1.72 % (2813983)Also succeeded, but the first one will report.
% 6.89/1.72 % (2814017)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=1065302396:i=134:sd=2:doe=on:ss=axioms:sgt=14_2993 on theBenchmark for (2993ds/134Mi)
% 6.89/1.72 % (2813985)Also succeeded, but the first one will report.
% 6.89/1.72 % (2814015)Also succeeded, but the first one will report.
% 6.89/1.72 % (2813984)Refutation found. Thanks to Tanya!
% 6.89/1.72 % SZS status Unsatisfiable for theBenchmark
% 6.89/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 6.89/1.73 % (2813984)------------------------------
% 6.89/1.73 % (2813984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.89/1.73 % (2813984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.73 % (2813984)CaDiCaL version: 2.1.3
% 6.89/1.73 % (2813984)Termination reason: Refutation
% 6.89/1.73 % (2813984)Time elapsed: 0.575 s
% 6.89/1.73 % (2813984)Peak memory usage: 127 MB
% 6.89/1.73 % (2813984)Instructions burned: 925 (million)
% 6.89/1.73 % (2813984)------------------------------
% 6.89/1.73 % (2813984)------------------------------
% 6.89/1.73 % (2813978)Success in time 0.887 s
% 6.89/1.73 % Vampire exiting
%------------------------------------------------------------------------------