%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n017.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 10:19:17 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 41 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 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/Axioms/HEN001-0.ax',less_equal_quotient) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',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(f57,plain,
! [X0,X1] :
( ~ quotient(identity,X1,X0)
| ~ less_equal(X0,idQa)
| less_equal(idQ_idQa,X1) ),
inference(resolution,[],[f15,f19]) ).
fof(f58,plain,
! [X0,X1] :
( ~ quotient(identity,X1,X0)
| ~ less_equal(X0,idQ_idQa)
| less_equal(idQ__idQ_idQa,X1) ),
inference(resolution,[],[f15,f20]) ).
fof(f67,plain,
! [X0,X1] :
( ~ quotient(identity,X0,X1)
| ~ less_equal(X0,a)
| less_equal(idQa,X1) ),
inference(resolution,[],[f16,f18]) ).
fof(f223,plain,
( ~ less_equal(idQa,idQa)
| less_equal(idQ_idQa,a) ),
inference(resolution,[],[f57,f18]) ).
fof(f232,plain,
less_equal(idQ_idQa,a),
inference(forward_subsumption_resolution,[],[f223,f23]) ).
fof(f245,plain,
( ~ less_equal(idQ_idQa,idQ_idQa)
| less_equal(idQ__idQ_idQa,idQa) ),
inference(resolution,[],[f58,f19]) ).
fof(f253,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(forward_subsumption_resolution,[],[f245,f23]) ).
fof(f258,plain,
( ~ less_equal(idQ_idQa,a)
| less_equal(idQa,idQ__idQ_idQa) ),
inference(resolution,[],[f67,f20]) ).
fof(f272,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(forward_subsumption_resolution,[],[f258,f232]) ).
fof(f275,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| idQa = idQ__idQ_idQa ),
inference(resolution,[],[f253,f6]) ).
fof(f276,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference(forward_subsumption_resolution,[],[f275,f21]) ).
fof(f460,plain,
$false,
inference(forward_subsumption_resolution,[],[f272,f276]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:46:35 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.46 % (2366338)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (2366346)dis+10_1_sil=32000:sp=arity:random_seed=1786873996:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (2366344)% WARNING: option uhcvi not known.
% 0.10/0.46 % (2366346) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2366338-2366346"...
% 0.10/0.46 % (2366346)...printing done.
% 0.10/0.46 % (2366346)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (2366346)------------------------------
% 0.10/0.46 % (2366346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (2366346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (2366346)CaDiCaL version: 2.1.3
% 0.10/0.46 % (2366346)Termination reason: Refutation
% 0.10/0.46 % (2366346)Time elapsed: 0.005 s
% 0.10/0.46 % (2366346)Peak memory usage: 11 MB
% 0.10/0.46 % (2366346)Instructions burned: 10 (million)
% 0.10/0.46 % (2366338)Success in time 0.034 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------