%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 15 unt; 4 def)
% Number of atoms : 96 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 92 ( 45 ~; 43 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_insert(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
fof(f5,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_insert(X1,X2,X3),X3)
| c_in(X0,X2,X3)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f7,negated_conjecture,
c_less(v_a,v_b,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f8,negated_conjecture,
c_less(v_b,v_c,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f9,negated_conjecture,
! [X0] :
( ~ c_in(v_b,X0,tc_IntDef_Oint)
| c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,X0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f10,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f11,plain,
! [X0,X1] :
( c_less(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f12,plain,
~ c_less(v_a,v_b,tc_IntDef_Oint),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f13,plain,
~ c_less(v_b,v_c,tc_IntDef_Oint),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f14,plain,
! [X0] :
( c_in(v_c,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[],[f5,f9]) ).
fof(f21,plain,
! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| v_b = v_c
| c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[],[f6,f14]) ).
fof(f23,definition,
( spl0_1
<=> v_b = v_c ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f25,plain,
( v_b = v_c
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f27,definition,
( spl0_2
<=> ! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f28,plain,
( ! [X0] :
( c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_c,X0,tc_IntDef_Oint) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f21,f27,f23]) ).
fof(f31,plain,
( ! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,X0,tc_IntDef_Oint)
| v_a = v_b )
| ~ spl0_2 ),
inference(resolution,[],[f28,f6]) ).
fof(f33,definition,
( spl0_3
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f35,plain,
( v_a = v_b
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,definition,
( spl0_4
<=> ! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,X0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f38,plain,
( ! [X0] :
( c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,X0,tc_IntDef_Oint) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f39,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f31,f27,f37,f33]) ).
fof(f43,plain,
( ~ c_less(v_b,v_b,tc_IntDef_Oint)
| ~ spl0_3 ),
inference(superposition,[],[f12,f35]) ).
fof(f46,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_3 ),
inference(resolution,[],[f43,f11]) ).
fof(f47,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f46,f10]) ).
fof(f48,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f47]) ).
fof(f50,plain,
( ! [X0] :
( c_in(v_a,c_uminus(X0,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| ~ c_in(v_c,X0,tc_IntDef_Oint) )
| ~ spl0_4 ),
inference(resolution,[],[f38,f2]) ).
fof(f59,plain,
( ! [X0] :
( ~ c_in(v_c,X0,tc_IntDef_Oint)
| ~ c_in(v_a,X0,tc_IntDef_Oint) )
| ~ spl0_4 ),
inference(resolution,[],[f50,f2]) ).
fof(f75,plain,
( ! [X0] : ~ c_in(v_a,c_insert(v_c,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_4 ),
inference(resolution,[],[f59,f5]) ).
fof(f89,plain,
( ~ c_less(v_b,v_b,tc_IntDef_Oint)
| ~ spl0_1 ),
inference(superposition,[],[f13,f25]) ).
fof(f99,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_1 ),
inference(resolution,[],[f89,f11]) ).
fof(f100,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f99,f10]) ).
fof(f101,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f104,plain,
( ! [X0] : ~ c_in(v_a,X0,tc_IntDef_Oint)
| ~ spl0_4 ),
inference(resolution,[],[f75,f4]) ).
fof(f118,plain,
( ! [X0] : c_in(v_a,X0,tc_IntDef_Oint)
| ~ spl0_4 ),
inference(resolution,[],[f104,f3]) ).
fof(f120,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f118,f104]) ).
fof(f121,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f120]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f101]) ).
cnf(s7,plain,
~ spl0_4,
inference(sat_conversion,[],[f121]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s2,s7,s3]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s5]) ).
fof(f133,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:57:12 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.12/0.45 % (2949719)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (2949725)% WARNING: option uhcvi not known.
% 0.12/0.45 % (2949725)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=91027605:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % (2949725) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2949719-2949725"...
% 0.12/0.45 % (2949725)...printing done.
% 0.12/0.45 % (2949725)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (2949725)------------------------------
% 0.12/0.45 % (2949725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (2949725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (2949725)CaDiCaL version: 2.1.3
% 0.12/0.45 % (2949725)Termination reason: Refutation
% 0.12/0.45 % (2949725)Time elapsed: 0.003 s
% 0.12/0.45 % (2949725)Peak memory usage: 12 MB
% 0.12/0.45 % (2949725)Instructions burned: 6 (million)
% 0.12/0.45 % (2949719)Success in time 0.033 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------