%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN009-2 : 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 : n003.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 10:19:08 AM UTC 2026
% Result : Unsatisfiable 2.69s 1.34s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 41 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f12,axiom,
! [X0] : quotient(X0,X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X0,X3,X4)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X1,X2)
| less_equal(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
fof(f16,axiom,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X2,X1,X3)
| ~ less_equal(X0,X1)
| ~ quotient(X2,X0,X4)
| less_equal(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
fof(f18,axiom,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f19,axiom,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f20,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
fof(f21,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).
fof(f23,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[],[f2,f12]) ).
fof(f54,plain,
! [X0,X1] :
( ~ quotient(identity,X1,X0)
| ~ less_equal(X0,idQa)
| less_equal(idQ_idQa,X1) ),
inference(resolution,[],[f15,f19]) ).
fof(f55,plain,
! [X0,X1] :
( ~ quotient(identity,X1,X0)
| ~ less_equal(X0,idQ_idQa)
| less_equal(idQ__idQ_idQa,X1) ),
inference(resolution,[],[f15,f20]) ).
fof(f64,plain,
! [X0,X1] :
( ~ quotient(identity,X0,X1)
| ~ less_equal(X0,a)
| less_equal(idQa,X1) ),
inference(resolution,[],[f16,f18]) ).
fof(f171,plain,
( ~ less_equal(idQa,idQa)
| less_equal(idQ_idQa,a) ),
inference(resolution,[],[f54,f18]) ).
fof(f179,plain,
less_equal(idQ_idQa,a),
inference(forward_subsumption_resolution,[],[f171,f23]) ).
fof(f192,plain,
( ~ less_equal(idQ_idQa,idQ_idQa)
| less_equal(idQ__idQ_idQa,idQa) ),
inference(resolution,[],[f55,f19]) ).
fof(f199,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(forward_subsumption_resolution,[],[f192,f23]) ).
fof(f204,plain,
( ~ less_equal(idQ_idQa,a)
| less_equal(idQa,idQ__idQ_idQa) ),
inference(resolution,[],[f64,f20]) ).
fof(f217,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(forward_subsumption_resolution,[],[f204,f179]) ).
fof(f220,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| idQa = idQ__idQ_idQa ),
inference(resolution,[],[f199,f6]) ).
fof(f221,plain,
idQa = idQ__idQ_idQa,
inference(forward_subsumption_resolution,[],[f220,f217]) ).
fof(f222,plain,
$false,
inference(forward_subsumption_resolution,[],[f221,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:52:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.69/1.34 % (337290)Input is clausal, will run a generic CNF schedule.
% 2.69/1.34 % (337298)lrs+10_1_sil=8000:sp=occurrence:random_seed=2561749019:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.69/1.34 % (337298)First to succeed.
% 2.69/1.34 % (337298)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-337290"
% 2.69/1.34 % (337299)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=789242388:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.69/1.34 % (337295)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=4081849995:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.69/1.34 % (337301)dis-21_1_sil=8000:lcm=predicate:random_seed=2167645517: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)
% 2.69/1.34 % (337296)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2075583755:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.69/1.34 % (337297)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=442597105:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.69/1.34 % (337300)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1760380508:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.69/1.34 % (337299)Also succeeded, but the first one will report.
% 2.69/1.34 % (337301)Instruction limit reached!
% 2.69/1.34 % (337301)------------------------------
% 2.69/1.34 % (337301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.34 % (337301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.34 % (337301)CaDiCaL version: 2.1.3
% 2.69/1.34 % (337301)Termination reason: Instruction limit
% 2.69/1.34 % (337301)Termination phase: Saturation
% 2.69/1.34 % (337301)Time elapsed: 0.061 s
% 2.69/1.34 % (337301)Peak memory usage: 88 MB
% 2.69/1.34 % (337301)Instructions burned: 118 (million)
% 2.69/1.34 % (337300)Instruction limit reached!
% 2.69/1.34 % (337300)------------------------------
% 2.69/1.34 % (337300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.34 % (337300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.34 % (337300)CaDiCaL version: 2.1.3
% 2.69/1.34 % (337300)Termination reason: Instruction limit
% 2.69/1.34 % (337300)Termination phase: Saturation
% 2.69/1.34 % (337300)Time elapsed: 0.105 s
% 2.69/1.34 % (337300)Peak memory usage: 88 MB
% 2.69/1.34 % (337300)Instructions burned: 182 (million)
% 2.69/1.34 % (337298)Refutation found. Thanks to Tanya!
% 2.69/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.69/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.34 % (337298)------------------------------
% 2.69/1.34 % (337298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.34 % (337298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.34 % (337298)CaDiCaL version: 2.1.3
% 2.69/1.34 % (337298)Termination reason: Refutation
% 2.69/1.34 % (337298)Time elapsed: 0.003 s
% 2.69/1.34 % (337298)Peak memory usage: 88 MB
% 2.69/1.34 % (337298)Instructions burned: 5 (million)
% 2.69/1.34 % (337298)------------------------------
% 2.69/1.34 % (337298)------------------------------
% 2.69/1.34 % (337290)Success in time 0.291 s
% 2.69/1.34 % Vampire exiting
%------------------------------------------------------------------------------