%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ062-2 : 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 : 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 12:32:07 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 41 ( 22 unt; 1 def)
% Number of atoms : 66 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 28 ~; 24 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
| c_in(X2,X0,X1)
| c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( c_in(c_inter(X2,X0,X1),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f3,axiom,
! [X0] :
( ~ c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
| c_in(X0,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_inter(X1,X2,X3),X3)
| c_in(X0,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_inter(X3,X1,X2),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f6,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7,axiom,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f8,negated_conjecture,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f9,negated_conjecture,
c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f10,negated_conjecture,
c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f11,plain,
c_emptyset = c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f13,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f14,negated_conjecture,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f15,plain,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(superposition,[],[f6,f12]) ).
fof(f16,plain,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(superposition,[],[f6,f13]) ).
fof(f23,plain,
c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(resolution,[],[f4,f15]) ).
fof(f24,plain,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(resolution,[],[f4,f16]) ).
fof(f45,definition,
( spl0_5
<=> c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f46,plain,
( c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( ~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| spl0_5 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f62,plain,
! [X0] :
( c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
| ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) ),
inference(superposition,[],[f5,f11]) ).
fof(f63,plain,
! [X0] :
( ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
| ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) ),
inference(forward_subsumption_resolution,[],[f62,f7]) ).
fof(f70,plain,
~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(resolution,[],[f63,f23]) ).
fof(f71,plain,
~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(resolution,[],[f63,f24]) ).
fof(f104,plain,
c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(resolution,[],[f3,f8]) ).
fof(f105,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f104,f47]) ).
fof(f106,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( c_in(X0,c_inter(X1,X2,X3),X3)
| c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3))
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
inference(resolution,[],[f1,f2]) ).
fof(f185,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
| c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3))
| c_in(X0,X2,X3) ),
inference(resolution,[],[f114,f4]) ).
fof(f190,plain,
( ! [X0,X1] :
( c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
| c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) )
| ~ spl0_5 ),
inference(resolution,[],[f185,f46]) ).
fof(f199,plain,
( ! [X0] : c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| ~ spl0_5 ),
inference(resolution,[],[f190,f70]) ).
fof(f200,plain,
( ! [X0] : c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
| ~ spl0_5 ),
inference(resolution,[],[f190,f71]) ).
fof(f220,plain,
( c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
| ~ spl0_5 ),
inference(superposition,[],[f14,f200]) ).
fof(f221,plain,
( c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
| ~ spl0_5 ),
inference(forward_demodulation,[],[f220,f9]) ).
fof(f222,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f221,f199]) ).
fof(f223,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f222]) ).
cnf(s82,plain,
spl0_5,
inference(sat_conversion,[],[f106]) ).
cnf(s172,plain,
~ spl0_5,
inference(sat_conversion,[],[f223]) ).
cnf(s173,plain,
$false,
inference(rat,[],[s82,s172]) ).
fof(f224,plain,
$false,
inference(avatar_sat_refutation,[],[s173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:40:12 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (988366)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (988373)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3688591620:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (988372)% WARNING: option uhcvi not known.
% 0.11/0.45 % (988373) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-988366-988373"...
% 0.11/0.45 % (988373)...printing done.
% 0.11/0.45 % (988372)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4005110806:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % (988373)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (988373)------------------------------
% 0.11/0.45 % (988373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (988373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (988373)CaDiCaL version: 2.1.3
% 0.11/0.45 % (988373)Termination reason: Refutation
% 0.11/0.45 % (988373)Time elapsed: 0.006 s
% 0.11/0.45 % (988373)Peak memory usage: 12 MB
% 0.11/0.45 % (988373)Instructions burned: 12 (million)
% 0.11/0.45 % (988366)Success in time 0.033 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------