%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG002-1 : 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 : 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 09:07:31 AM UTC 2026
% Result : Unsatisfiable 3.85s 1.34s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 42 ( 11 unt; 3 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 99 ( 52 ~; 44 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f2,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_abelian) ).
fof(f5,axiom,
! [X2,X0,X1] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_inverse) ).
fof(f6,axiom,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| product(X0,X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_and_identity) ).
fof(f7,axiom,
! [X0] :
( ~ greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_greater_than_0) ).
fof(f8,axiom,
! [X0] :
( ~ product(X0,X0,additive_identity)
| ~ greater_than_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greater_than_0_square) ).
fof(f9,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_product) ).
fof(f10,axiom,
! [X0] :
( product(X0,X0,additive_identity)
| greater_than_0(X0)
| greater_than_0(additive_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_inverse) ).
fof(f11,axiom,
! [X2,X0,X1] :
( product(X2,X2,additive_identity)
| ~ product(X0,X0,additive_identity)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_to_0) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| ~ greater_than_0(X0)
| ~ greater_than_0(X1)
| greater_than_0(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_greater_than_0) ).
fof(f13,axiom,
greater_than_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_greater_than_0) ).
fof(f14,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
fof(f20,definition,
( spl0_1
<=> greater_than_0(additive_inverse(multiplicative_identity)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| ~ greater_than_0(additive_inverse(X1))
| greater_than_0(additive_inverse(X2))
| ~ greater_than_0(X0) ),
inference(resolution,[],[f12,f5]) ).
fof(f45,plain,
! [X0,X1] :
( ~ product(X0,X1,multiplicative_identity)
| ~ product(X0,X0,additive_identity) ),
inference(resolution,[],[f11,f2]) ).
fof(f60,plain,
! [X0,X1] :
( ~ product(X1,X0,multiplicative_identity)
| ~ product(X0,X0,additive_identity) ),
inference(resolution,[],[f45,f9]) ).
fof(f69,plain,
! [X0] :
( ~ product(multiplicative_inverse(X0),multiplicative_inverse(X0),additive_identity)
| product(X0,X0,additive_identity) ),
inference(resolution,[],[f60,f6]) ).
fof(f104,plain,
! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_identity))
| greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0) ),
inference(resolution,[],[f37,f1]) ).
fof(f106,plain,
! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(X0)
| product(X0,X0,additive_identity) ),
inference(resolution,[],[f37,f6]) ).
fof(f108,plain,
! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(X0) ),
inference(forward_subsumption_resolution,[],[f106,f8]) ).
fof(f109,plain,
! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(X0) ),
inference(forward_subsumption_resolution,[],[f104,f7]) ).
fof(f111,definition,
( spl0_7
<=> ! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| ~ greater_than_0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f112,plain,
( ! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| ~ greater_than_0(X0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f108,f111,f20]) ).
fof(f115,definition,
( spl0_8
<=> ! [X0] : ~ greater_than_0(X0) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f116,plain,
( ! [X0] : ~ greater_than_0(X0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_8
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f109,f20,f115]) ).
fof(f154,plain,
! [X0] :
( greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| greater_than_0(multiplicative_inverse(X0))
| product(X0,X0,additive_identity) ),
inference(resolution,[],[f69,f10]) ).
fof(f205,plain,
( ! [X0] :
( greater_than_0(multiplicative_inverse(X0))
| product(X0,X0,additive_identity)
| ~ greater_than_0(X0) )
| ~ spl0_7 ),
inference(resolution,[],[f154,f112]) ).
fof(f207,plain,
( ! [X0] :
( greater_than_0(multiplicative_inverse(X0))
| ~ greater_than_0(X0) )
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f205,f8]) ).
fof(f219,plain,
( ~ greater_than_0(a)
| ~ spl0_7 ),
inference(resolution,[],[f207,f14]) ).
fof(f220,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f219,f13]) ).
fof(f221,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f220]) ).
fof(f253,plain,
( $false
| ~ spl0_8 ),
inference(resolution,[],[f116,f13]) ).
fof(f254,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f253]) ).
cnf(s7,plain,
( spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f113]) ).
cnf(s8,plain,
( ~ spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f118]) ).
cnf(s12,plain,
~ spl0_7,
inference(sat_conversion,[],[f221]) ).
cnf(s20,plain,
~ spl0_8,
inference(sat_conversion,[],[f254]) ).
cnf(s22,plain,
~ spl0_1,
inference(rat,[],[s8,s20]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s7,s12,s22]) ).
fof(f259,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n008.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Mon Sep 28 19:17:24 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running first-order theorem proving
% 0.10/0.25 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
% 3.85/1.34 % (2542994)Input is clausal, will run a generic CNF schedule.
% 3.85/1.34 % (2543069)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2349706650:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.85/1.34 % (2543074)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=290761197:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.85/1.34 % (2543070)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4148930958:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.85/1.34 % (2543073)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4099622099:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.85/1.34 % (2543072)lrs+10_1_sil=8000:sp=occurrence:random_seed=921351792:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.85/1.34 % (2543068)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=3325317170:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.85/1.34 % (2543076)dis-21_1_sil=8000:lcm=predicate:random_seed=1110479356: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)
% 3.85/1.34 % (2543073)First to succeed.
% 3.85/1.34 % (2543073)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2542994"
% 3.85/1.34 % (2543072)Also succeeded, but the first one will report.
% 3.85/1.34 % (2543074)Also succeeded, but the first one will report.
% 3.85/1.34 % (2543076)Instruction limit reached!
% 3.85/1.34 % (2543076)------------------------------
% 3.85/1.34 % (2543076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.34 % (2543076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.34 % (2543076)CaDiCaL version: 2.1.3
% 3.85/1.34 % (2543076)Termination reason: Instruction limit
% 3.85/1.34 % (2543076)Termination phase: Saturation
% 3.85/1.34 % (2543076)Time elapsed: 0.064 s
% 3.85/1.34 % (2543076)Peak memory usage: 88 MB
% 3.85/1.34 % (2543076)Instructions burned: 119 (million)
% 3.85/1.34 % (2543124)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=3290312629:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.85/1.34 % (2543124)Refutation not found, incomplete strategy
% 3.85/1.34 % (2543124)------------------------------
% 3.85/1.34 % (2543124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.34 % (2543124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.34 % (2543124)CaDiCaL version: 2.1.3
% 3.85/1.34 % (2543124)Termination reason: Refutation not found, incomplete strategy
% 3.85/1.34 % (2543124)Time elapsed: 0.001 s
% 3.85/1.34 % (2543124)Peak memory usage: 87 MB
% 3.85/1.34 % (2543073)Refutation found. Thanks to Tanya!
% 3.85/1.34 % SZS status Unsatisfiable for theBenchmark
% 3.85/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.85/1.34 % (2543073)------------------------------
% 3.85/1.34 % (2543073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.34 % (2543073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.34 % (2543073)CaDiCaL version: 2.1.3
% 3.85/1.34 % (2543073)Termination reason: Refutation
% 3.85/1.34 % (2543073)Time elapsed: 0.006 s
% 3.85/1.34 % (2543073)Peak memory usage: 88 MB
% 3.85/1.34 % (2543073)Instructions burned: 6 (million)
% 3.85/1.34 % (2543073)------------------------------
% 3.85/1.34 % (2543073)------------------------------
% 3.85/1.34 % (2542994)Success in time 0.452 s
% 3.85/1.34 % Vampire exiting
%------------------------------------------------------------------------------