%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:35:47 AM UTC 2026
% Result : Unsatisfiable 6.25s 1.67s
% Output : Refutation 6.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 10 ( 8 unt; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X2,X4,X6)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X5,X6)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
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/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
fof(f17,axiom,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f23,negated_conjecture,
~ product(x,x,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_equalities) ).
fof(f40,plain,
~ sum(additive_identity,multiply(x,x),x),
inference(unit_resulting_resolution,[],[f13,f2,f5,f5,f23]) ).
fof(f849,plain,
$false,
inference(unit_resulting_resolution,[],[f9,f20,f17,f8,f2,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n010.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:03:17 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.21 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
% 6.25/1.67 % (2331673)Input is clausal, will run a generic CNF schedule.
% 6.25/1.67 % (2331791)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=540664602:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.25/1.67 % (2331792)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4024977217:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.25/1.67 % (2331793)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2019736404:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.25/1.67 % (2331795)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=463335669:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.25/1.67 % (2331794)lrs+10_1_sil=8000:sp=occurrence:random_seed=113229483:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.25/1.67 % (2331794)Refutation not found, incomplete strategy
% 6.25/1.67 % (2331794)------------------------------
% 6.25/1.67 % (2331794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.67 % (2331794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.67 % (2331794)CaDiCaL version: 2.1.3
% 6.25/1.67 % (2331794)Termination reason: Refutation not found, incomplete strategy
% 6.25/1.67 % (2331794)Time elapsed: 0.001 s
% 6.25/1.67 % (2331794)Peak memory usage: 87 MB
% 6.25/1.67 % (2331797)dis-21_1_sil=8000:lcm=predicate:random_seed=2615728285: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)
% 6.25/1.67 % (2331796)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2638093945:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.25/1.67 % (2331795)Instruction limit reached!
% 6.25/1.67 % (2331795)------------------------------
% 6.25/1.67 % (2331795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.67 % (2331795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.67 % (2331795)CaDiCaL version: 2.1.3
% 6.25/1.67 % (2331795)Termination reason: Instruction limit
% 6.25/1.67 % (2331795)Termination phase: Saturation
% 6.25/1.67 % (2331795)Time elapsed: 0.057 s
% 6.25/1.67 % (2331795)Peak memory usage: 87 MB
% 6.25/1.67 % (2331795)Instructions burned: 114 (million)
% 6.25/1.67 % (2331797)Instruction limit reached!
% 6.25/1.67 % (2331797)------------------------------
% 6.25/1.67 % (2331797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.67 % (2331797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.67 % (2331797)CaDiCaL version: 2.1.3
% 6.25/1.67 % (2331797)Termination reason: Instruction limit
% 6.25/1.67 % (2331797)Termination phase: Saturation
% 6.25/1.67 % (2331797)Time elapsed: 0.058 s
% 6.25/1.67 % (2331797)Peak memory usage: 88 MB
% 6.25/1.67 % (2331797)Instructions burned: 118 (million)
% 6.25/1.67 % (2331796)Instruction limit reached!
% 6.25/1.67 % (2331796)------------------------------
% 6.25/1.67 % (2331796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.67 % (2331796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.67 % (2331796)CaDiCaL version: 2.1.3
% 6.25/1.67 % (2331796)Termination reason: Instruction limit
% 6.25/1.67 % (2331796)Termination phase: Saturation
% 6.25/1.67 % (2331796)Time elapsed: 0.128 s
% 6.25/1.67 % (2331796)Peak memory usage: 88 MB
% 6.25/1.67 % (2331796)Instructions burned: 181 (million)
% 6.25/1.67 % (2331805)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=953185261:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.25/1.67 % (2331805)Refutation not found, incomplete strategy
% 6.25/1.67 % (2331805)------------------------------
% 6.25/1.67 % (2331805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.67 % (2331805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.67 % (2331805)CaDiCaL version: 2.1.3
% 6.25/1.67 % (2331805)Termination reason: Refutation not found, incomplete strategy
% 6.25/1.67 % (2331805)Time elapsed: 0.002 s
% 6.25/1.67 % (2331805)Peak memory usage: 88 MB
% 6.25/1.67 % (2331805)Instructions burned: 1 (million)
% 6.25/1.67 % (2331806)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1889178965: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)
% 6.25/1.67 % (2331794)------------------------------
% 6.25/1.67 % (2331794)------------------------------
% 6.25/1.67 % (2331806)First to succeed.
% 6.25/1.67 % (2331806)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2331673"
% 6.25/1.67 % (2331807)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3315342035:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 6.25/1.67 % (2331791)Also succeeded, but the first one will report.
% 6.25/1.67 % (2331818)lrs+10_64_to=lpo:sil=8000:random_seed=292026339:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.25/1.67 % (2331818)Also succeeded, but the first one will report.
% 6.25/1.67 % (2331805)------------------------------
% 6.25/1.67 % (2331805)------------------------------
% 6.25/1.67 % (2331807)Instruction limit reached!
% 6.25/1.67 % (2331807)------------------------------
% 6.25/1.67 % (2331807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.67 % (2331807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.67 % (2331807)CaDiCaL version: 2.1.3
% 6.25/1.67 % (2331807)Termination reason: Instruction limit
% 6.25/1.67 % (2331807)Termination phase: Saturation
% 6.25/1.67 % (2331807)Time elapsed: 0.138 s
% 6.25/1.67 % (2331807)Peak memory usage: 88 MB
% 6.25/1.67 % (2331807)Instructions burned: 221 (million)
% 6.25/1.67 % (2331806)Refutation found. Thanks to Tanya!
% 6.25/1.67 % SZS status Unsatisfiable for theBenchmark
% 6.25/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 6.25/1.67 % (2331806)------------------------------
% 6.25/1.67 % (2331806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.67 % (2331806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.67 % (2331806)CaDiCaL version: 2.1.3
% 6.25/1.67 % (2331806)Termination reason: Refutation
% 6.25/1.67 % (2331806)Time elapsed: 0.031 s
% 6.25/1.67 % (2331806)Peak memory usage: 88 MB
% 6.25/1.67 % (2331806)Instructions burned: 37 (million)
% 6.25/1.67 % (2331806)------------------------------
% 6.25/1.67 % (2331806)------------------------------
% 6.25/1.67 % (2331673)Success in time 0.82 s
% 6.25/1.67 % Vampire exiting
%------------------------------------------------------------------------------