%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT005-1 : 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 : n010.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 09:36:34 AM UTC 2026
% Result : Unsatisfiable 3.20s 1.61s
% Output : Refutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 47 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 31 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X2,X3)
| defined(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property2) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_domain) ).
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(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,axiom,
defined(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ad_defined) ).
fof(f20,axiom,
identity_map(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_identity_map) ).
fof(f21,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_is_d) ).
fof(f22,plain,
d != domain(a),
inference(reorient_equations,[],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( defined(domain(X0),X1)
| ~ defined(X0,X1) ),
inference(resolution,[],[f3,f14]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X0 = X2
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(resolution,[],[f18,f17]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| X0 = X2
| ~ identity_map(X1) ),
inference(forward_subsumption_resolution,[],[f34,f2]) ).
fof(f86,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| ~ identity_map(X1)
| ~ identity_map(X0)
| X0 = X1 ),
inference(resolution,[],[f36,f16]) ).
fof(f120,plain,
! [X0,X1] :
( ~ identity_map(X0)
| ~ identity_map(domain(X1))
| domain(X1) = X0
| ~ defined(X1,X0) ),
inference(resolution,[],[f86,f26]) ).
fof(f123,plain,
! [X0,X1] :
( domain(X1) = X0
| ~ identity_map(X0)
| ~ defined(X1,X0) ),
inference(forward_subsumption_resolution,[],[f120,f10]) ).
fof(f128,plain,
! [X0] :
( ~ defined(a,X0)
| ~ identity_map(X0)
| d != X0 ),
inference(superposition,[],[f22,f123]) ).
fof(f146,plain,
( ~ identity_map(d)
| d != d ),
inference(resolution,[],[f128,f19]) ).
fof(f154,plain,
~ identity_map(d),
inference(trivial_inequality_removal,[],[f146]) ).
fof(f155,plain,
$false,
inference(forward_subsumption_resolution,[],[f154,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.29 % Computer : n010.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8046.5625MB
% 0.09/0.29 % OS : Linux 6.8.0-71-generic
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Sep 28 21:13:18 UTC 2026
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.31/0.36 Running first-order theorem proving
% 0.31/0.36 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
% 3.20/1.61 % (2344528)Input is clausal, will run a generic CNF schedule.
% 3.20/1.61 % (2344537)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3457101397:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.20/1.61 % (2344537)First to succeed.
% 3.20/1.61 % (2344537)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2344528"
% 3.20/1.61 % (2344534)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2825851108:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.20/1.61 % (2344533)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=1483862430:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.20/1.61 % (2344536)lrs+10_1_sil=8000:sp=occurrence:random_seed=1679277128:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.20/1.61 % (2344535)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1631935988:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.20/1.61 % (2344538)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1366317204:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.20/1.61 % (2344536)Also succeeded, but the first one will report.
% 3.20/1.61 % (2344539)dis-21_1_sil=8000:lcm=predicate:random_seed=4286221834: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)
% 3.20/1.61 % (2344538)Also succeeded, but the first one will report.
% 3.20/1.61 % (2344539)Instruction limit reached!
% 3.20/1.61 % (2344539)------------------------------
% 3.20/1.61 % (2344539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.61 % (2344539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.61 % (2344539)CaDiCaL version: 2.1.3
% 3.20/1.61 % (2344539)Termination reason: Instruction limit
% 3.20/1.61 % (2344539)Termination phase: Saturation
% 3.20/1.61 % (2344539)Time elapsed: 0.065 s
% 3.20/1.61 % (2344539)Peak memory usage: 88 MB
% 3.20/1.61 % (2344539)Instructions burned: 118 (million)
% 3.20/1.61 % (2344537)Refutation found. Thanks to Tanya!
% 3.20/1.61 % SZS status Unsatisfiable for theBenchmark
% 3.20/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 3.20/1.61 % (2344537)------------------------------
% 3.20/1.61 % (2344537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.20/1.61 % (2344537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/1.61 % (2344537)CaDiCaL version: 2.1.3
% 3.20/1.61 % (2344537)Termination reason: Refutation
% 3.20/1.61 % (2344537)Time elapsed: 0.003 s
% 3.20/1.61 % (2344537)Peak memory usage: 88 MB
% 3.20/1.61 % (2344537)Instructions burned: 6 (million)
% 3.20/1.61 % (2344537)------------------------------
% 3.20/1.61 % (2344537)------------------------------
% 3.20/1.61 % (2344528)Success in time 0.298 s
% 3.20/1.61 % Vampire exiting
%------------------------------------------------------------------------------