%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 09:36:07 AM UTC 2026
% Result : Unsatisfiable 1.00s 0.45s
% Output : Refutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 63 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 71 ( 36 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
fof(f2,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X5,X6)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X1,X2)
| sum(X2,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2)
| ~ sum(X0,X5,X6)
| product(X2,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity5) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2)
| ~ sum(X5,X1,X6)
| product(X2,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity7) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
fof(f23,negated_conjecture,
~ product(x,add(x,y),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equations) ).
fof(f33,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[],[f4,f2]) ).
fof(f47,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X3,X1,inverse(X0))
| ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| sum(X4,X2,additive_identity) ),
inference(resolution,[],[f9,f20]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| multiply(X1,X0) = X2 ),
inference(resolution,[],[f33,f22]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2)
| ~ sum(X0,multiply(X3,X1),X5)
| product(X4,X2,X5) ),
inference(resolution,[],[f13,f2]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2)
| ~ sum(multiply(X3,X0),X1,X5)
| product(X4,X2,X5) ),
inference(resolution,[],[f15,f2]) ).
fof(f282,plain,
! [X2,X0,X1] :
( ~ product(X0,additive_identity,X2)
| ~ product(X0,inverse(X0),X1)
| sum(X2,X1,additive_identity) ),
inference(resolution,[],[f47,f5]) ).
fof(f487,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,multiply(additive_identity,X1),X3)
| product(X0,X2,X3) ),
inference(resolution,[],[f87,f6]) ).
fof(f508,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,additive_identity,X1)
| ~ sum(multiply(X2,X0),additive_identity,X3)
| product(X2,X1,X3) ),
inference(resolution,[],[f99,f6]) ).
fof(f1015,plain,
! [X0,X1] :
( ~ product(X0,inverse(X0),X1)
| sum(multiply(X0,additive_identity),X1,additive_identity) ),
inference(resolution,[],[f282,f2]) ).
fof(f1788,plain,
! [X2,X0,X1] :
( ~ sum(X0,multiply(additive_identity,X1),X2)
| product(X0,add(X0,X1),X2) ),
inference(resolution,[],[f487,f1]) ).
fof(f1855,plain,
! [X2,X0,X1] :
( ~ sum(multiply(X0,X1),additive_identity,X2)
| product(X0,X1,X2) ),
inference(resolution,[],[f508,f6]) ).
fof(f6275,plain,
! [X0] : sum(multiply(X0,additive_identity),additive_identity,additive_identity),
inference(resolution,[],[f1015,f20]) ).
fof(f6288,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(resolution,[],[f6275,f1855]) ).
fof(f6435,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[],[f6288,f58]) ).
fof(f9709,plain,
! [X2,X0,X1] :
( ~ sum(X0,additive_identity,X2)
| product(X0,add(X0,X1),X2) ),
inference(forward_demodulation,[],[f1788,f6435]) ).
fof(f9710,plain,
! [X0,X1] : product(X0,add(X0,X1),X0),
inference(resolution,[],[f9709,f6]) ).
fof(f9746,plain,
$false,
inference(backward_subsumption_resolution,[],[f23,f9710]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n001.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 21:09:34 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.00/0.45 % (749136)Will run a generic schedule for satisfiability detection.
% 1.00/0.45 % (749155)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2414619461:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.00/0.45 % (749150)% WARNING: option uhcvi not known.
% 1.00/0.45 % (749150)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2923764347:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.00/0.45 % (749151)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3346925033:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.00/0.45 % (749148)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=605087520_2999 on theBenchmark for (2999ds/0Mi)
% 1.00/0.45 % (749152)dis+10_1_sil=32000:sp=arity:random_seed=2777729410:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.00/0.45 % (749153)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1432028825:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.00/0.45 % (749154)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=340729327:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.00/0.45 % TRYING [1]
% 1.00/0.45 % TRYING [2]
% 1.00/0.45 % TRYING [3]
% 1.00/0.45 % TRYING [4]
% 1.00/0.45 % (749155)Instruction limit reached!
% 1.00/0.45 % (749155)------------------------------
% 1.00/0.45 % (749155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.45 % (749155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.45 % (749155)CaDiCaL version: 2.1.3
% 1.00/0.45 % (749155)Termination reason: Instruction limit
% 1.00/0.45 % (749155)Termination phase: Saturation
% 1.00/0.45 % (749155)Time elapsed: 0.052 s
% 1.00/0.45 % (749155)Peak memory usage: 12 MB
% 1.00/0.45 % (749155)Instructions burned: 161 (million)
% 1.00/0.45 % TRYING [5]
% 1.00/0.45 % (749181)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3136825967:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.00/0.45 % TRYING [1]
% 1.00/0.45 % TRYING [2]
% 1.00/0.45 % TRYING [3]
% 1.00/0.45 % (749153)Instruction limit reached!
% 1.00/0.45 % (749153)------------------------------
% 1.00/0.45 % (749153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.45 % (749153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.45 % (749153)CaDiCaL version: 2.1.3
% 1.00/0.45 % (749153)Termination reason: Instruction limit
% 1.00/0.45 % (749153)Termination phase: Saturation
% 1.00/0.45 % (749153)Time elapsed: 0.062 s
% 1.00/0.45 % (749153)Peak memory usage: 12 MB
% 1.00/0.45 % (749153)Instructions burned: 117 (million)
% 1.00/0.45 % (749152)Instruction limit reached!
% 1.00/0.45 % (749152)------------------------------
% 1.00/0.45 % (749152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.45 % (749152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.45 % TRYING [4]
% 1.00/0.45 % (749152)CaDiCaL version: 2.1.3
% 1.00/0.45 % (749152)Termination reason: Instruction limit
% 1.00/0.45 % (749152)Termination phase: Saturation
% 1.00/0.45 % (749152)Time elapsed: 0.064 s
% 1.00/0.45 % (749152)Peak memory usage: 12 MB
% 1.00/0.45 % (749152)Instructions burned: 103 (million)
% 1.00/0.45 % (749154)Instruction limit reached!
% 1.00/0.45 % (749154)------------------------------
% 1.00/0.45 % (749154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.45 % (749154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.45 % (749154)CaDiCaL version: 2.1.3
% 1.00/0.45 % (749154)Termination reason: Instruction limit
% 1.00/0.45 % (749154)Termination phase: Saturation
% 1.00/0.45 % (749154)Time elapsed: 0.080 s
% 1.00/0.45 % (749154)Peak memory usage: 12 MB
% 1.00/0.45 % (749154)Instructions burned: 133 (million)
% 1.00/0.45 % (749192)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2478223558:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.00/0.45 % (749195)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1216274999:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.00/0.45 % TRYING [5]
% 1.00/0.45 % (749199)ott-21_1_sil=16000:fs=off:random_seed=3885993719:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.00/0.45 % TRYING [6]
% 1.00/0.45 % TRYING [6]
% 1.00/0.45 % (749192)Instruction limit reached!
% 1.00/0.45 % (749192)------------------------------
% 1.00/0.45 % (749192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.45 % (749192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.45 % (749192)CaDiCaL version: 2.1.3
% 1.00/0.45 % (749192)Termination reason: Instruction limit
% 1.00/0.45 % (749192)Termination phase: Saturation
% 1.00/0.45 % (749192)Time elapsed: 0.102 s
% 1.00/0.45 % (749192)Peak memory usage: 12 MB
% 1.00/0.45 % (749192)Instructions burned: 135 (million)
% 1.00/0.45 % (749150) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-749136-749150"...
% 1.00/0.45 % (749150)...printing done.
% 1.00/0.45 % (749150)Refutation found. Thanks to Tanya!
% 1.00/0.45 % SZS status Unsatisfiable for theBenchmark
% 1.00/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 1.00/0.45 % (749150)------------------------------
% 1.00/0.45 % (749150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.45 % (749150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.45 % (749150)CaDiCaL version: 2.1.3
% 1.00/0.45 % (749150)Termination reason: Refutation
% 1.00/0.45 % (749150)Time elapsed: 0.187 s
% 1.00/0.45 % (749150)Peak memory usage: 13 MB
% 1.00/0.45 % (749150)Instructions burned: 305 (million)
% 1.00/0.45 % (749136)Success in time 0.233 s
% 1.00/0.45 % Vampire exiting
%------------------------------------------------------------------------------