%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT011-1 : 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 : n020.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 09:36:36 AM UTC 2026
% Result : Unsatisfiable 2.91s 1.18s
% Output : Refutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 34 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_domain) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_codomain) ).
fof(f16,axiom,
! [X0,X1] :
( ~ identity_map(X0)
| ~ defined(X0,X1)
| product(X0,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( ~ identity_map(X1)
| ~ defined(X0,X1)
| product(X0,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity2) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_well_defined) ).
fof(f19,negated_conjecture,
domain(domain(a)) != domain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_is_idempotent) ).
fof(f20,plain,
domain(a) != domain(domain(a)),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ product(X0,domain(X0),X1)
| X0 = X1 ),
inference(resolution,[],[f18,f14]) ).
fof(f22,plain,
! [X0,X1] :
( ~ product(codomain(X0),X0,X1)
| X0 = X1 ),
inference(resolution,[],[f18,f15]) ).
fof(f34,plain,
! [X0,X1] :
( product(codomain(X0),X1,X1)
| ~ defined(codomain(X0),X1) ),
inference(resolution,[],[f16,f11]) ).
fof(f36,plain,
! [X0,X1] :
( product(X0,domain(X1),X0)
| ~ defined(X0,domain(X1)) ),
inference(resolution,[],[f17,f10]) ).
fof(f48,plain,
! [X0] :
( ~ defined(codomain(X0),domain(codomain(X0)))
| codomain(X0) = domain(codomain(X0)) ),
inference(resolution,[],[f34,f21]) ).
fof(f49,plain,
! [X0] : codomain(X0) = domain(codomain(X0)),
inference(forward_subsumption_resolution,[],[f48,f12]) ).
fof(f81,plain,
! [X0] :
( ~ defined(codomain(domain(X0)),domain(X0))
| domain(X0) = codomain(domain(X0)) ),
inference(resolution,[],[f36,f22]) ).
fof(f84,plain,
! [X0] : domain(X0) = codomain(domain(X0)),
inference(forward_subsumption_resolution,[],[f81,f13]) ).
fof(f93,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(superposition,[],[f49,f84]) ).
fof(f157,plain,
domain(a) != domain(a),
inference(superposition,[],[f20,f93]) ).
fof(f169,plain,
$false,
inference(trivial_inequality_removal,[],[f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.17 % Computer : n020.cluster.edu
% 0.13/0.17 % Model : x86_64 x86_64
% 0.13/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.17 % Memory : 8046.5625MB
% 0.13/0.17 % OS : Linux 6.8.0-71-generic
% 0.13/0.17 % CPULimit : 300
% 0.13/0.17 % WCLimit : 300
% 0.13/0.17 % DateTime : Mon Sep 28 21:14:04 UTC 2026
% 0.13/0.17 % CPUTime :
% 0.13/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.21 Running first-order theorem proving
% 0.13/0.21 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
% 2.91/1.18 % (567802)Input is clausal, will run a generic CNF schedule.
% 2.91/1.18 % (567895)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=403277841:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.91/1.18 % (567895)First to succeed.
% 2.91/1.18 % (567895)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-567802"
% 2.91/1.18 % (567890)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3580955640:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.91/1.18 % (567887)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=3892678124:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.91/1.18 % (567892)lrs+10_1_sil=8000:sp=occurrence:random_seed=2344768000:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.91/1.18 % (567893)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3228480049:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.91/1.18 % (567891)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4068695884:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.91/1.18 % (567893)Also succeeded, but the first one will report.
% 2.91/1.18 % (567892)Also succeeded, but the first one will report.
% 2.91/1.18 % (567896)dis-21_1_sil=8000:lcm=predicate:random_seed=3140865891: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)
% 2.91/1.18 % (567896)Also succeeded, but the first one will report.
% 2.91/1.18 % (567895)Refutation found. Thanks to Tanya!
% 2.91/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.91/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.91/1.18 % (567895)------------------------------
% 2.91/1.18 % (567895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.18 % (567895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.18 % (567895)CaDiCaL version: 2.1.3
% 2.91/1.18 % (567895)Termination reason: Refutation
% 2.91/1.18 % (567895)Time elapsed: 0.004 s
% 2.91/1.18 % (567895)Peak memory usage: 88 MB
% 2.91/1.18 % (567895)Instructions burned: 7 (million)
% 2.91/1.18 % (567895)------------------------------
% 2.91/1.18 % (567895)------------------------------
% 2.91/1.18 % (567802)Success in time 0.334 s
% 2.91/1.18 % Vampire exiting
%------------------------------------------------------------------------------