%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT018-1 : 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 : n017.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 09:36:39 AM UTC 2026
% Result : Unsatisfiable 3.54s 1.18s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 49 ( 14 unt; 2 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 114 ( 57 ~; 55 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_composition) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property2) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom3) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ identity_map(X1)
| ~ defined(X1,X2)
| ~ defined(X0,X1)
| defined(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom6) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
fof(f11,axiom,
! [X0] : identity_map(codomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).
fof(f12,axiom,
! [X0] : defined(X0,domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
fof(f13,axiom,
! [X0] : defined(codomain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
fof(f16,axiom,
! [X0,X1] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity2) ).
fof(f19,axiom,
defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f20,axiom,
defined(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f21,negated_conjecture,
~ defined(a,compose(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_bc_exists) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ defined(domain(X0),X1)
| ~ defined(X2,domain(X0))
| defined(X2,X1) ),
inference(resolution,[],[f9,f10]) ).
fof(f185,definition,
( spl0_9
<=> defined(domain(a),compose(b,c)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f186,plain,
( defined(domain(a),compose(b,c))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f187,plain,
( ~ defined(domain(a),compose(b,c))
| spl0_9 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f196,plain,
( ! [X0,X1] :
( ~ defined(X0,compose(b,c))
| ~ product(X1,domain(a),X0) )
| spl0_9 ),
inference(resolution,[],[f187,f3]) ).
fof(f213,plain,
( ! [X0] : ~ product(X0,domain(a),codomain(compose(b,c)))
| spl0_9 ),
inference(resolution,[],[f196,f13]) ).
fof(f219,plain,
( ~ identity_map(domain(a))
| ~ defined(codomain(compose(b,c)),domain(a))
| spl0_9 ),
inference(resolution,[],[f213,f17]) ).
fof(f220,plain,
( ~ defined(codomain(compose(b,c)),domain(a))
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f219,f10]) ).
fof(f230,plain,
( ! [X0,X1] :
( ~ product(X1,codomain(compose(b,c)),X0)
| ~ defined(X0,domain(a)) )
| spl0_9 ),
inference(resolution,[],[f220,f3]) ).
fof(f373,plain,
( ! [X0] :
( ~ defined(X0,domain(a))
| ~ identity_map(codomain(compose(b,c)))
| ~ defined(X0,codomain(compose(b,c))) )
| spl0_9 ),
inference(resolution,[],[f230,f17]) ).
fof(f375,plain,
( ! [X0] :
( ~ defined(X0,codomain(compose(b,c)))
| ~ defined(X0,domain(a)) )
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f373,f11]) ).
fof(f579,definition,
( spl0_12
<=> defined(a,codomain(compose(b,c))) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f580,plain,
( defined(a,codomain(compose(b,c)))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f581,plain,
( ~ defined(a,codomain(compose(b,c)))
| spl0_12 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f587,plain,
( ! [X0,X1] :
( ~ product(codomain(compose(b,c)),X1,X0)
| ~ defined(a,X0) )
| spl0_12 ),
inference(resolution,[],[f581,f6]) ).
fof(f598,plain,
( ! [X0] :
( ~ defined(a,X0)
| ~ identity_map(codomain(compose(b,c)))
| ~ defined(codomain(compose(b,c)),X0) )
| spl0_12 ),
inference(resolution,[],[f587,f16]) ).
fof(f600,plain,
( ! [X0] :
( ~ defined(a,X0)
| ~ defined(codomain(compose(b,c)),X0) )
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f598,f11]) ).
fof(f603,plain,
( ~ defined(codomain(compose(b,c)),b)
| spl0_12 ),
inference(resolution,[],[f600,f19]) ).
fof(f626,plain,
( ! [X0,X1] :
( ~ product(b,X1,X0)
| ~ defined(codomain(compose(b,c)),X0) )
| spl0_12 ),
inference(resolution,[],[f603,f6]) ).
fof(f643,plain,
( ! [X0] :
( ~ defined(codomain(compose(b,c)),compose(b,X0))
| ~ defined(b,X0) )
| spl0_12 ),
inference(resolution,[],[f626,f1]) ).
fof(f691,plain,
( ~ defined(b,c)
| spl0_12 ),
inference(resolution,[],[f643,f13]) ).
fof(f697,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f691,f20]) ).
fof(f698,plain,
spl0_12,
inference(avatar_contradiction_clause,[],[f697]) ).
fof(f706,plain,
( ~ defined(a,domain(a))
| spl0_9
| ~ spl0_12 ),
inference(resolution,[],[f580,f375]) ).
fof(f708,plain,
( $false
| spl0_9
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f706,f12]) ).
fof(f709,plain,
( spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f708]) ).
fof(f711,plain,
( ! [X0] :
( ~ defined(X0,domain(a))
| defined(X0,compose(b,c)) )
| ~ spl0_9 ),
inference(resolution,[],[f186,f42]) ).
fof(f727,plain,
( defined(a,compose(b,c))
| ~ spl0_9 ),
inference(resolution,[],[f711,f12]) ).
fof(f733,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f727,f21]) ).
fof(f734,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f733]) ).
cnf(s9,plain,
spl0_12,
inference(sat_conversion,[],[f698]) ).
cnf(s10,plain,
( spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f709]) ).
cnf(s11,plain,
~ spl0_9,
inference(sat_conversion,[],[f734]) ).
cnf(s12,plain,
~ spl0_12,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s9,s12]) ).
fof(f735,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:09:07 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 3.54/1.18 % (4035408)Input is clausal, will run a generic CNF schedule.
% 3.54/1.18 % (4035462)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3145669943:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.54/1.18 % (4035461)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2831927130:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.54/1.18 % (4035465)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1720014923:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.54/1.18 % (4035460)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=3977740522:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.54/1.18 % (4035463)lrs+10_1_sil=8000:sp=occurrence:random_seed=3068910710:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.54/1.18 % (4035464)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1890665805:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.54/1.18 % (4035466)dis-21_1_sil=8000:lcm=predicate:random_seed=3185100753: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)
% 3.54/1.18 % (4035465)First to succeed.
% 3.54/1.18 % (4035465)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4035408"
% 3.54/1.18 % (4035464)Instruction limit reached!
% 3.54/1.18 % (4035464)------------------------------
% 3.54/1.18 % (4035464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.18 % (4035464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.18 % (4035464)CaDiCaL version: 2.1.3
% 3.54/1.18 % (4035464)Termination reason: Instruction limit
% 3.54/1.18 % (4035464)Termination phase: Saturation
% 3.54/1.18 % (4035464)Time elapsed: 0.063 s
% 3.54/1.18 % (4035464)Peak memory usage: 88 MB
% 3.54/1.18 % (4035464)Instructions burned: 115 (million)
% 3.54/1.18 % (4035463)Instruction limit reached!
% 3.54/1.18 % (4035463)------------------------------
% 3.54/1.18 % (4035463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.18 % (4035463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.18 % (4035463)CaDiCaL version: 2.1.3
% 3.54/1.18 % (4035463)Termination reason: Instruction limit
% 3.54/1.18 % (4035463)Termination phase: Saturation
% 3.54/1.18 % (4035463)Time elapsed: 0.065 s
% 3.54/1.18 % (4035463)Peak memory usage: 88 MB
% 3.54/1.18 % (4035463)Instructions burned: 109 (million)
% 3.54/1.18 % (4035466)Instruction limit reached!
% 3.54/1.18 % (4035466)------------------------------
% 3.54/1.18 % (4035466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.18 % (4035466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.18 % (4035466)CaDiCaL version: 2.1.3
% 3.54/1.18 % (4035466)Termination reason: Instruction limit
% 3.54/1.18 % (4035466)Termination phase: Saturation
% 3.54/1.18 % (4035466)Time elapsed: 0.075 s
% 3.54/1.18 % (4035466)Peak memory usage: 88 MB
% 3.54/1.18 % (4035466)Instructions burned: 117 (million)
% 3.54/1.18 % (4035475)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3694832367: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)
% 3.54/1.18 % (4035474)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=3761369699:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.54/1.18 % (4035474)Refutation not found, incomplete strategy
% 3.54/1.18 % (4035474)------------------------------
% 3.54/1.18 % (4035474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.18 % (4035474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.18 % (4035474)CaDiCaL version: 2.1.3
% 3.54/1.18 % (4035474)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.18 % (4035474)Time elapsed: 0.001 s
% 3.54/1.18 % (4035474)Peak memory usage: 88 MB
% 3.54/1.18 % (4035474)Instructions burned: 1 (million)
% 3.54/1.18 % (4035475)Also succeeded, but the first one will report.
% 3.54/1.18 % (4035476)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3848843620:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.54/1.18 % (4035465)Refutation found. Thanks to Tanya!
% 3.54/1.18 % SZS status Unsatisfiable for theBenchmark
% 3.54/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.18 % (4035465)------------------------------
% 3.54/1.18 % (4035465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.18 % (4035465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.18 % (4035465)CaDiCaL version: 2.1.3
% 3.54/1.18 % (4035465)Termination reason: Refutation
% 3.54/1.18 % (4035465)Time elapsed: 0.025 s
% 3.54/1.18 % (4035465)Peak memory usage: 89 MB
% 3.54/1.18 % (4035465)Instructions burned: 33 (million)
% 3.54/1.18 % (4035465)------------------------------
% 3.54/1.18 % (4035465)------------------------------
% 3.54/1.18 % (4035408)Success in time 0.418 s
% 3.54/1.18 % Vampire exiting
%------------------------------------------------------------------------------