%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO013-3 : 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 : n018.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 5.25s 1.47s
% Output : Refutation 5.25s
% 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(f24,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
fof(f25,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
fof(f26,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity1) ).
fof(f27,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity2) ).
fof(f28,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
fof(f34,plain,
~ sum(additive_identity,z,y),
inference(unit_resulting_resolution,[],[f21,f5,f28]) ).
fof(f45,plain,
sum(y,x,multiplicative_identity),
inference(unit_resulting_resolution,[],[f3,f24]) ).
fof(f1156,plain,
~ product(multiplicative_identity,add(y,z),y),
inference(unit_resulting_resolution,[],[f16,f25,f26,f1,f34]) ).
fof(f1389,plain,
product(multiplicative_identity,add(y,z),y),
inference(unit_resulting_resolution,[],[f13,f27,f6,f1,f45]) ).
fof(f1508,plain,
$false,
inference(forward_subsumption_resolution,[],[f1389,f1156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n018.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 : Mon Sep 28 21:06:10 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 5.25/1.47 % (3785957)Input is clausal, will run a generic CNF schedule.
% 5.25/1.47 % (3786037)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=319186711:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.25/1.47 % (3786044)dis-21_1_sil=8000:lcm=predicate:random_seed=2770631709: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)
% 5.25/1.47 % (3786043)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1318279807:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.25/1.47 % (3786041)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=419944054:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.25/1.47 % (3786035)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=637655685:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.25/1.47 % (3786040)lrs+10_1_sil=8000:sp=occurrence:random_seed=2798256766:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.25/1.47 % (3786038)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3783397290:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.25/1.47 % (3786044)Instruction limit reached!
% 5.25/1.47 % (3786044)------------------------------
% 5.25/1.47 % (3786044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.47 % (3786044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.47 % (3786044)CaDiCaL version: 2.1.3
% 5.25/1.47 % (3786044)Termination reason: Instruction limit
% 5.25/1.47 % (3786044)Termination phase: Saturation
% 5.25/1.47 % (3786044)Time elapsed: 0.059 s
% 5.25/1.47 % (3786044)Peak memory usage: 88 MB
% 5.25/1.47 % (3786044)Instructions burned: 119 (million)
% 5.25/1.47 % (3786041)Instruction limit reached!
% 5.25/1.47 % (3786041)------------------------------
% 5.25/1.47 % (3786041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.47 % (3786041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.47 % (3786041)CaDiCaL version: 2.1.3
% 5.25/1.47 % (3786041)Termination reason: Instruction limit
% 5.25/1.47 % (3786041)Termination phase: Saturation
% 5.25/1.47 % (3786041)Time elapsed: 0.065 s
% 5.25/1.47 % (3786041)Peak memory usage: 88 MB
% 5.25/1.47 % (3786041)Instructions burned: 114 (million)
% 5.25/1.47 % (3786040)Instruction limit reached!
% 5.25/1.47 % (3786040)------------------------------
% 5.25/1.47 % (3786040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.47 % (3786040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.47 % (3786040)CaDiCaL version: 2.1.3
% 5.25/1.47 % (3786040)Termination reason: Instruction limit
% 5.25/1.47 % (3786040)Termination phase: Saturation
% 5.25/1.47 % (3786040)Time elapsed: 0.066 s
% 5.25/1.47 % (3786040)Peak memory usage: 88 MB
% 5.25/1.47 % (3786040)Instructions burned: 107 (million)
% 5.25/1.47 % (3786043)Instruction limit reached!
% 5.25/1.47 % (3786043)------------------------------
% 5.25/1.47 % (3786043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.47 % (3786043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.47 % (3786043)CaDiCaL version: 2.1.3
% 5.25/1.47 % (3786043)Termination reason: Instruction limit
% 5.25/1.47 % (3786043)Termination phase: Saturation
% 5.25/1.47 % (3786043)Time elapsed: 0.114 s
% 5.25/1.47 % (3786043)Peak memory usage: 88 MB
% 5.25/1.47 % (3786043)Instructions burned: 181 (million)
% 5.25/1.47 % (3786095)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=2920263886:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.25/1.47 % (3786098)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3953294412: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)
% 5.25/1.47 % (3786095)Refutation not found, incomplete strategy
% 5.25/1.47 % (3786095)------------------------------
% 5.25/1.47 % (3786095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.47 % (3786095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.47 % (3786095)CaDiCaL version: 2.1.3
% 5.25/1.47 % (3786095)Termination reason: Refutation not found, incomplete strategy
% 5.25/1.47 % (3786095)Time elapsed: 0.017 s
% 5.25/1.47 % (3786095)Peak memory usage: 88 MB
% 5.25/1.47 % (3786095)Instructions burned: 24 (million)
% 5.25/1.47 % (3786098)First to succeed.
% 5.25/1.47 % (3786098)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3785957"
% 5.25/1.47 % (3786109)lrs+10_64_to=lpo:sil=8000:random_seed=2402022:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.25/1.47 % (3786101)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3252524684:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.25/1.47 % (3786109)Instruction limit reached!
% 5.25/1.47 % (3786109)------------------------------
% 5.25/1.47 % (3786109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.47 % (3786109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.47 % (3786109)CaDiCaL version: 2.1.3
% 5.25/1.47 % (3786109)Termination reason: Instruction limit
% 5.25/1.47 % (3786109)Termination phase: Saturation
% 5.25/1.47 % (3786109)Time elapsed: 0.075 s
% 5.25/1.47 % (3786109)Peak memory usage: 89 MB
% 5.25/1.47 % (3786109)Instructions burned: 126 (million)
% 5.25/1.47 % (3786101)Instruction limit reached!
% 5.25/1.47 % (3786101)------------------------------
% 5.25/1.47 % (3786101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.47 % (3786101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.47 % (3786101)CaDiCaL version: 2.1.3
% 5.25/1.47 % (3786101)Termination reason: Instruction limit
% 5.25/1.47 % (3786101)Termination phase: Saturation
% 5.25/1.47 % (3786101)Time elapsed: 0.110 s
% 5.25/1.47 % (3786101)Peak memory usage: 89 MB
% 5.25/1.47 % (3786101)Instructions burned: 220 (million)
% 5.25/1.47 % (3786095)------------------------------
% 5.25/1.47 % (3786095)------------------------------
% 5.25/1.47 % (3786114)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1454330275:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.25/1.47 % (3786098)Refutation found. Thanks to Tanya!
% 5.25/1.47 % SZS status Unsatisfiable for theBenchmark
% 5.25/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 5.25/1.47 % (3786098)------------------------------
% 5.25/1.47 % (3786098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.47 % (3786098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.47 % (3786098)CaDiCaL version: 2.1.3
% 5.25/1.47 % (3786098)Termination reason: Refutation
% 5.25/1.47 % (3786098)Time elapsed: 0.041 s
% 5.25/1.47 % (3786098)Peak memory usage: 89 MB
% 5.25/1.47 % (3786098)Instructions burned: 75 (million)
% 5.25/1.47 % (3786098)------------------------------
% 5.25/1.47 % (3786098)------------------------------
% 5.25/1.47 % (3785957)Success in time 0.669 s
% 5.25/1.47 % Vampire exiting
%------------------------------------------------------------------------------