%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% 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 09:35:52 AM UTC 2026
% Result : Unsatisfiable 0.35s 2.61s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 28 ( 2 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f3,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X2,X4,X6)
| ~ sum(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ sum(X0,X5,X6)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity5) ).
fof(f16,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X5,X1,X6)
| ~ sum(X3,X1,X4)
| ~ product(X0,X3,X5)
| ~ product(X2,X4,X6)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity8) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f23,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
fof(f24,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
fof(f25,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity1) ).
fof(f26,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity2) ).
fof(f27,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
fof(f33,plain,
~ sum(additive_identity,z,y),
inference(unit_resulting_resolution,[],[f21,f5,f27]) ).
fof(f44,plain,
sum(y,x,multiplicative_identity),
inference(unit_resulting_resolution,[],[f3,f23]) ).
fof(f1125,plain,
~ product(multiplicative_identity,add(y,z),y),
inference(unit_resulting_resolution,[],[f16,f24,f25,f1,f33]) ).
fof(f1340,plain,
product(multiplicative_identity,add(y,z),y),
inference(unit_resulting_resolution,[],[f13,f26,f6,f1,f44]) ).
fof(f1459,plain,
$false,
inference(forward_subsumption_resolution,[],[f1340,f1125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 % Computer : n010.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Mon Sep 28 21:04:17 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.30/0.35 Running first-order theorem proving
% 0.30/0.35 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
% 0.35/2.61 % (2334787)Input is clausal, will run a generic CNF schedule.
% 0.35/2.61 % (2334798)dis-21_1_sil=8000:lcm=predicate:random_seed=428747474: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)
% 0.35/2.61 % (2334798)Instruction limit reached!
% 0.35/2.61 % (2334798)------------------------------
% 0.35/2.61 % (2334798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.61 % (2334798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.61 % (2334798)CaDiCaL version: 2.1.3
% 0.35/2.61 % (2334798)Termination reason: Instruction limit
% 0.35/2.61 % (2334798)Termination phase: Saturation
% 0.35/2.61 % (2334798)Time elapsed: 0.048 s
% 0.35/2.61 % (2334798)Peak memory usage: 88 MB
% 0.35/2.61 % (2334798)Instructions burned: 118 (million)
% 0.35/2.61 % (2334792)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=3892617610:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.35/2.61 % (2334793)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1773103028:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.35/2.61 % (2334796)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1426035945:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.35/2.61 % (2334795)lrs+10_1_sil=8000:sp=occurrence:random_seed=1241042245:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.35/2.61 % (2334794)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1534629230:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.35/2.61 % (2334797)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=174534817:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.35/2.61 % (2334795)Instruction limit reached!
% 0.35/2.61 % (2334795)------------------------------
% 0.35/2.61 % (2334795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.61 % (2334795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.61 % (2334795)CaDiCaL version: 2.1.3
% 0.35/2.61 % (2334795)Termination reason: Instruction limit
% 0.35/2.61 % (2334795)Termination phase: Saturation
% 0.35/2.61 % (2334795)Time elapsed: 0.097 s
% 0.35/2.61 % (2334795)Peak memory usage: 88 MB
% 0.35/2.61 % (2334795)Instructions burned: 108 (million)
% 0.35/2.61 % (2334796)Instruction limit reached!
% 0.35/2.61 % (2334796)------------------------------
% 0.35/2.61 % (2334796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.61 % (2334796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.61 % (2334796)CaDiCaL version: 2.1.3
% 0.35/2.61 % (2334796)Termination reason: Instruction limit
% 0.35/2.61 % (2334796)Termination phase: Saturation
% 0.35/2.61 % (2334796)Time elapsed: 0.101 s
% 0.35/2.61 % (2334796)Peak memory usage: 88 MB
% 0.35/2.61 % (2334796)Instructions burned: 115 (million)
% 0.35/2.61 % (2334797)Instruction limit reached!
% 0.35/2.61 % (2334797)------------------------------
% 0.35/2.61 % (2334797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.61 % (2334797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.61 % (2334797)CaDiCaL version: 2.1.3
% 0.35/2.61 % (2334797)Termination reason: Instruction limit
% 0.35/2.61 % (2334797)Termination phase: Saturation
% 0.35/2.61 % (2334797)Time elapsed: 0.163 s
% 0.35/2.61 % (2334797)Peak memory usage: 89 MB
% 0.35/2.61 % (2334797)Instructions burned: 181 (million)
% 0.35/2.61 % (2334802)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=2476086665:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.35/2.61 % (2334802)Refutation not found, incomplete strategy
% 0.35/2.61 % (2334802)------------------------------
% 0.35/2.61 % (2334802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.61 % (2334802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.61 % (2334802)CaDiCaL version: 2.1.3
% 0.35/2.61 % (2334802)Termination reason: Refutation not found, incomplete strategy
% 0.35/2.61 % (2334802)Time elapsed: 0.023 s
% 0.35/2.61 % (2334802)Peak memory usage: 88 MB
% 0.35/2.61 % (2334802)Instructions burned: 22 (million)
% 0.35/2.61 % (2334807)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1014308505: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)
% 0.35/2.61 % (2334808)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1304547385:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 0.35/2.61 % (2334807)First to succeed.
% 0.35/2.61 % (2334807)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2334787"
% 0.35/2.61 % (2334809)lrs+10_64_to=lpo:sil=8000:random_seed=1322114936:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 0.35/2.61 % (2334802)------------------------------
% 0.35/2.61 % (2334802)------------------------------
% 0.35/2.61 % (2334808)Instruction limit reached!
% 0.35/2.61 % (2334808)------------------------------
% 0.35/2.61 % (2334808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.61 % (2334808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.61 % (2334808)CaDiCaL version: 2.1.3
% 0.35/2.61 % (2334808)Termination reason: Instruction limit
% 0.35/2.61 % (2334808)Termination phase: Saturation
% 0.35/2.61 % (2334808)Time elapsed: 0.184 s
% 0.35/2.61 % (2334808)Peak memory usage: 89 MB
% 0.35/2.61 % (2334808)Instructions burned: 220 (million)
% 0.35/2.61 % (2334809)Instruction limit reached!
% 0.35/2.61 % (2334809)------------------------------
% 0.35/2.61 % (2334809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.61 % (2334809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.61 % (2334809)CaDiCaL version: 2.1.3
% 0.35/2.61 % (2334809)Termination reason: Instruction limit
% 0.35/2.61 % (2334809)Termination phase: Saturation
% 0.35/2.61 % (2334809)Time elapsed: 0.118 s
% 0.35/2.61 % (2334809)Peak memory usage: 89 MB
% 0.35/2.61 % (2334809)Instructions burned: 126 (million)
% 0.35/2.61 % (2334814)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4168924304:avsq=on:i=194:fgj=on:bd=preordered_2991 on theBenchmark for (2991ds/194Mi)
% 0.35/2.61 % (2334807)Refutation found. Thanks to Tanya!
% 0.35/2.61 % SZS status Unsatisfiable for theBenchmark
% 0.35/2.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/2.61 % (2334807)------------------------------
% 0.35/2.61 % (2334807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.35/2.61 % (2334807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/2.61 % (2334807)CaDiCaL version: 2.1.3
% 0.35/2.61 % (2334807)Termination reason: Refutation
% 0.35/2.61 % (2334807)Time elapsed: 0.065 s
% 0.35/2.61 % (2334807)Peak memory usage: 89 MB
% 0.35/2.61 % (2334807)Instructions burned: 74 (million)
% 0.35/2.61 % (2334807)------------------------------
% 0.35/2.61 % (2334807)------------------------------
% 0.35/2.61 % (2334787)Success in time 1.15 s
% 0.35/2.61 % Vampire exiting
%------------------------------------------------------------------------------