%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT012-1 : 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 : n004.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 09:36:37 AM UTC 2026
% Result : Unsatisfiable 3.59s 1.23s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 22 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 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 : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
fof(f13,axiom,
! [X0] : defined(codomain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_codomain) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity2) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_well_defined) ).
fof(f19,negated_conjecture,
codomain(domain(a)) != domain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_domain_is_domain) ).
fof(f20,plain,
domain(a) != codomain(domain(a)),
inference(reorient_equations,[],[f19]) ).
fof(f35,plain,
! [X0,X1] :
( ~ product(codomain(X0),X0,X1)
| X0 = X1 ),
inference(resolution,[],[f18,f15]) ).
fof(f90,plain,
! [X0] :
( codomain(X0) = X0
| ~ identity_map(X0)
| ~ defined(codomain(X0),X0) ),
inference(resolution,[],[f35,f17]) ).
fof(f94,plain,
! [X0] :
( codomain(X0) = X0
| ~ identity_map(X0) ),
inference(forward_subsumption_resolution,[],[f90,f13]) ).
fof(f95,plain,
( domain(a) != domain(a)
| ~ identity_map(domain(a)) ),
inference(superposition,[],[f20,f94]) ).
fof(f101,plain,
~ identity_map(domain(a)),
inference(trivial_inequality_removal,[],[f95]) ).
fof(f102,plain,
$false,
inference(forward_subsumption_resolution,[],[f101,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n004.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 21:13:22 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running first-order theorem proving
% 0.11/0.24 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
% 3.59/1.23 % (783104)Input is clausal, will run a generic CNF schedule.
% 3.59/1.23 % (783128)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=1977074967:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.59/1.23 % (783136)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2192035684:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.59/1.23 % (783130)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1052294774:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.59/1.23 % (783133)lrs+10_1_sil=8000:sp=occurrence:random_seed=797948088:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.59/1.23 % (783138)dis-21_1_sil=8000:lcm=predicate:random_seed=402386787: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)
% 3.59/1.23 % (783134)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=405760083:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.59/1.23 % (783132)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2555542910:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.59/1.23 % (783134)First to succeed.
% 3.59/1.23 % (783136)Also succeeded, but the first one will report.
% 3.59/1.23 % (783133)Also succeeded, but the first one will report.
% 3.59/1.23 % (783134)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-783104"
% 3.59/1.23 % (783138)Instruction limit reached!
% 3.59/1.23 % (783138)------------------------------
% 3.59/1.23 % (783138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.23 % (783138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.23 % (783138)CaDiCaL version: 2.1.3
% 3.59/1.23 % (783138)Termination reason: Instruction limit
% 3.59/1.23 % (783138)Termination phase: Saturation
% 3.59/1.23 % (783138)Time elapsed: 0.066 s
% 3.59/1.23 % (783138)Peak memory usage: 88 MB
% 3.59/1.23 % (783138)Instructions burned: 117 (million)
% 3.59/1.23 % (783218)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=2647231335:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.59/1.23 % (783218)Refutation not found, incomplete strategy
% 3.59/1.23 % (783218)------------------------------
% 3.59/1.23 % (783218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.23 % (783218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.23 % (783218)CaDiCaL version: 2.1.3
% 3.59/1.23 % (783218)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.23 % (783218)Time elapsed: 0.001 s
% 3.59/1.23 % (783218)Peak memory usage: 88 MB
% 3.59/1.23 % (783134)Refutation found. Thanks to Tanya!
% 3.59/1.23 % SZS status Unsatisfiable for theBenchmark
% 3.59/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.23 % (783134)------------------------------
% 3.59/1.23 % (783134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.23 % (783134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.23 % (783134)CaDiCaL version: 2.1.3
% 3.59/1.23 % (783134)Termination reason: Refutation
% 3.59/1.23 % (783134)Time elapsed: 0.004 s
% 3.59/1.23 % (783134)Peak memory usage: 88 MB
% 3.59/1.23 % (783134)Instructions burned: 4 (million)
% 3.59/1.23 % (783134)------------------------------
% 3.59/1.23 % (783134)------------------------------
% 3.59/1.23 % (783104)Success in time 0.436 s
% 3.59/1.23 % Vampire exiting
%------------------------------------------------------------------------------