%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT014-4 : 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 : n007.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 09:36:38 AM UTC 2026
% Result : Unsatisfiable 2.78s 1.19s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 22 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f7,axiom,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
fof(f12,axiom,
there_exists(codomain(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_codomain_exists) ).
fof(f13,negated_conjecture,
codomain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_is_idempotent) ).
fof(f14,plain,
codomain(a) != codomain(codomain(a)),
inference(reorient_equations,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( compose(X1,codomain(X0)) = X1
| ~ there_exists(compose(X1,X0)) ),
inference(superposition,[],[f10,f7]) ).
fof(f26,plain,
! [X0] :
( ~ there_exists(compose(X0,codomain(a)))
| domain(X0) != codomain(a) ),
inference(superposition,[],[f14,f7]) ).
fof(f76,plain,
! [X0] :
( ~ there_exists(X0)
| domain(X0) != codomain(a)
| ~ there_exists(compose(X0,a)) ),
inference(superposition,[],[f26,f22]) ).
fof(f88,plain,
! [X0] :
( ~ there_exists(compose(X0,a))
| ~ there_exists(X0) ),
inference(forward_subsumption_resolution,[],[f76,f7]) ).
fof(f128,plain,
( ~ there_exists(a)
| ~ there_exists(codomain(a)) ),
inference(superposition,[],[f88,f11]) ).
fof(f130,plain,
~ there_exists(codomain(a)),
inference(forward_subsumption_resolution,[],[f128,f5]) ).
fof(f132,plain,
$false,
inference(forward_subsumption_resolution,[],[f130,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT014-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:11:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.78/1.19 % (2831705)Input is clausal, will run a generic CNF schedule.
% 2.78/1.19 % (2831800)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4052156282:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.78/1.19 % (2831800)First to succeed.
% 2.78/1.19 % (2831800)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2831705"
% 2.78/1.19 % (2831795)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2402509041:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.78/1.19 % (2831793)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=2961889315:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.78/1.19 % (2831797)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1414137259:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.78/1.19 % (2831804)dis-21_1_sil=8000:lcm=predicate:random_seed=2157656017: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)
% 2.78/1.19 % (2831804)Refutation not found, incomplete strategy
% 2.78/1.19 % (2831804)------------------------------
% 2.78/1.19 % (2831804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.19 % (2831804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.19 % (2831804)CaDiCaL version: 2.1.3
% 2.78/1.19 % (2831804)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.19 % (2831804)Time elapsed: 0.002 s
% 2.78/1.19 % (2831804)Peak memory usage: 88 MB
% 2.78/1.19 % (2831804)Instructions burned: 1 (million)
% 2.78/1.19 % (2831798)lrs+10_1_sil=8000:sp=occurrence:random_seed=4050066165:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.78/1.19 % (2831802)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3315053645:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.78/1.19 % (2831798)Also succeeded, but the first one will report.
% 2.78/1.19 % (2831802)Also succeeded, but the first one will report.
% 2.78/1.19 % (2831800)Refutation found. Thanks to Tanya!
% 2.78/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.19 % (2831800)------------------------------
% 2.78/1.19 % (2831800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.19 % (2831800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.19 % (2831800)CaDiCaL version: 2.1.3
% 2.78/1.19 % (2831800)Termination reason: Refutation
% 2.78/1.19 % (2831800)Time elapsed: 0.003 s
% 2.78/1.19 % (2831800)Peak memory usage: 88 MB
% 2.78/1.19 % (2831800)Instructions burned: 5 (million)
% 2.78/1.19 % (2831800)------------------------------
% 2.78/1.19 % (2831800)------------------------------
% 2.78/1.19 % (2831705)Success in time 0.312 s
% 2.78/1.19 % Vampire exiting
%------------------------------------------------------------------------------