%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET820-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:44:41 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 20 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f2,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_insert(X1,X2,X3),X3)
| c_in(X0,X2,X3)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f4,negated_conjecture,
v_P(v_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f5,negated_conjecture,
! [X0,X1] :
( ~ c_in(X0,X1,tc_IntDef_Oint)
| c_in(v_x(X1),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0,X1] :
( ~ v_P(v_x(X1))
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f8,plain,
! [X2,X0,X1] :
( c_in(v_x(c_insert(X0,X1,tc_IntDef_Oint)),X1,tc_IntDef_Oint)
| ~ c_in(X2,c_insert(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint)
| v_x(c_insert(X0,X1,tc_IntDef_Oint)) = X0 ),
inference(resolution,[],[f3,f5]) ).
fof(f11,plain,
! [X0,X1] :
( ~ c_in(X1,c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
| v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0 ),
inference(resolution,[],[f8,f1]) ).
fof(f19,plain,
! [X0] : v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0,
inference(resolution,[],[f11,f2]) ).
fof(f21,plain,
! [X0,X1] :
( ~ v_P(X0)
| ~ c_in(X1,c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(superposition,[],[f6,f19]) ).
fof(f27,plain,
! [X0] : ~ c_in(X0,c_insert(v_a,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolution,[],[f21,f4]) ).
fof(f42,plain,
$false,
inference(resolution,[],[f27,f2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET820-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n005.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 02:53:47 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 Running first-order model finding
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.44 % (384997)Will run a generic schedule for satisfiability detection.
% 0.13/0.44 % (385006)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1231437202:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.44 % (385006) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-384997-385006"...
% 0.13/0.44 % (385006)...printing done.
% 0.13/0.44 % (385006)Refutation found. Thanks to Tanya!
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.44 % (385006)------------------------------
% 0.13/0.44 % (385006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.44 % (385006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.44 % (385006)CaDiCaL version: 2.1.3
% 0.13/0.44 % (385006)Termination reason: Refutation
% 0.13/0.44 % (385006)Time elapsed: 0.001 s
% 0.13/0.44 % (385006)Peak memory usage: 11 MB
% 0.13/0.44 % (385006)Instructions burned: 2 (million)
% 0.13/0.44 % (384997)Success in time 0.025 s
% 0.13/0.44 % Vampire exiting
%------------------------------------------------------------------------------