%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT009-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 0.22s 1.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 29 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 19 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f6,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f7,axiom,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
fof(f20,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).
fof(f21,negated_conjecture,
domain(compose(a,b)) != domain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
fof(f31,plain,
! [X0] :
( ~ there_exists(compose(compose(a,b),X0))
| codomain(X0) != domain(b) ),
inference(superposition,[],[f21,f7]) ).
fof(f36,plain,
! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(superposition,[],[f5,f7]) ).
fof(f37,plain,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(X1) ),
inference(forward_subsumption_resolution,[],[f36,f6]) ).
fof(f44,plain,
! [X0] :
( ~ there_exists(compose(a,compose(b,X0)))
| codomain(X0) != domain(b) ),
inference(superposition,[],[f31,f9]) ).
fof(f52,plain,
( ~ there_exists(compose(a,b))
| domain(b) != codomain(domain(b)) ),
inference(superposition,[],[f44,f10]) ).
fof(f53,plain,
domain(b) != codomain(domain(b)),
inference(forward_subsumption_resolution,[],[f52,f20]) ).
fof(f57,plain,
! [X0] :
( ~ there_exists(compose(X0,domain(b)))
| domain(X0) != domain(b) ),
inference(superposition,[],[f53,f7]) ).
fof(f65,plain,
( ~ there_exists(b)
| domain(b) != domain(b) ),
inference(superposition,[],[f57,f10]) ).
fof(f68,plain,
~ there_exists(b),
inference(trivial_inequality_removal,[],[f65]) ).
fof(f85,plain,
there_exists(b),
inference(resolution,[],[f37,f20]) ).
fof(f89,plain,
$false,
inference(forward_subsumption_resolution,[],[f85,f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT009-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.19 % Computer : n015.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Mon Sep 28 21:16:32 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.23 Running first-order theorem proving
% 0.13/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/1.30 % (3027821)Input is clausal, will run a generic CNF schedule.
% 0.22/1.30 % (3027921)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=2986141910:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.22/1.30 % (3027927)dis-21_1_sil=8000:lcm=predicate:random_seed=4247414471: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)
% 0.22/1.30 % (3027922)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2261537832:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.22/1.30 % (3027925)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=70406873:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.22/1.30 % (3027926)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=607732520:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.22/1.30 % (3027923)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2544011340:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.22/1.30 % (3027924)lrs+10_1_sil=8000:sp=occurrence:random_seed=2931210918:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.22/1.30 % (3027925)First to succeed.
% 0.22/1.30 % (3027925)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3027821"
% 0.22/1.30 % (3027926)Also succeeded, but the first one will report.
% 0.22/1.30 % (3027924)Also succeeded, but the first one will report.
% 0.22/1.30 % (3027927)Instruction limit reached!
% 0.22/1.30 % (3027927)------------------------------
% 0.22/1.30 % (3027927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.30 % (3027927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.30 % (3027927)CaDiCaL version: 2.1.3
% 0.22/1.30 % (3027927)Termination reason: Instruction limit
% 0.22/1.30 % (3027927)Termination phase: Saturation
% 0.22/1.30 % (3027927)Time elapsed: 0.058 s
% 0.22/1.30 % (3027927)Peak memory usage: 89 MB
% 0.22/1.30 % (3027927)Instructions burned: 118 (million)
% 0.22/1.30 % (3027935)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=1809953844:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.22/1.31 % (3027935)Also succeeded, but the first one will report.
% 0.22/1.31 % (3027925)Refutation found. Thanks to Tanya!
% 0.22/1.31 % SZS status Unsatisfiable for theBenchmark
% 0.22/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/1.31 % (3027925)------------------------------
% 0.22/1.31 % (3027925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.31 % (3027925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.31 % (3027925)CaDiCaL version: 2.1.3
% 0.22/1.31 % (3027925)Termination reason: Refutation
% 0.22/1.31 % (3027925)Time elapsed: 0.004 s
% 0.22/1.31 % (3027925)Peak memory usage: 88 MB
% 0.22/1.31 % (3027925)Instructions burned: 3 (million)
% 0.22/1.31 % (3027925)------------------------------
% 0.22/1.31 % (3027925)------------------------------
% 0.22/1.31 % (3027821)Success in time 0.43 s
% 0.22/1.31 % Vampire exiting
%------------------------------------------------------------------------------