%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:31:26 PM UTC 2026
% Result : Unsatisfiable 0.18s 1.50s
% Output : Refutation 0.18s
% 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7,axiom,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f17,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(f21,definition,
( spl0_1
<=> c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f23,plain,
( ~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
| spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f30,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(f31,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,[],[f30,f7]) ).
fof(f32,plain,
~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(resolution,[],[f31,f17]) ).
fof(f33,plain,
c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
inference(resolution,[],[f3,f8]) ).
fof(f34,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f33,f23]) ).
fof(f35,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f34]) ).
fof(f36,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(f40,plain,
c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
inference(resolution,[],[f16,f4]) ).
fof(f41,plain,
~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
inference(resolution,[],[f40,f31]) ).
fof(f42,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,[],[f36,f4]) ).
fof(f50,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_1 ),
inference(resolution,[],[f42,f22]) ).
fof(f52,plain,
( ! [X0] : 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)) = c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
| ~ spl0_1 ),
inference(resolution,[],[f50,f32]) ).
fof(f53,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_1 ),
inference(resolution,[],[f50,f41]) ).
fof(f58,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_1 ),
inference(superposition,[],[f14,f53]) ).
fof(f59,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_1 ),
inference(forward_demodulation,[],[f58,f9]) ).
fof(f60,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f59,f52]) ).
fof(f61,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f35]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n007.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 22:36:25 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/1.50 % (1842698)Input is clausal, will run a generic CNF schedule.
% 0.18/1.50 % (1842709)dis-21_1_sil=8000:lcm=predicate:random_seed=3800236117: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)
% 0.18/1.50 % (1842709)Refutation not found, incomplete strategy
% 0.18/1.50 % (1842709)------------------------------
% 0.18/1.50 % (1842709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (1842709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (1842709)CaDiCaL version: 2.1.3
% 0.18/1.50 % (1842709)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.50 % (1842709)Time elapsed: 0.001 s
% 0.18/1.50 % (1842709)Peak memory usage: 88 MB
% 0.18/1.50 % (1842709)Instructions burned: 1 (million)
% 0.18/1.50 % (1842703)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=799921285:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.18/1.50 % (1842704)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=154110686:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.18/1.50 % (1842706)lrs+10_1_sil=8000:sp=occurrence:random_seed=1447748252:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.18/1.50 % (1842705)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3122160792:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.18/1.50 % (1842707)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=679092063:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.18/1.50 % (1842708)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=199909477:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.18/1.50 % (1842706)First to succeed.
% 0.18/1.50 % (1842707)Also succeeded, but the first one will report.
% 0.18/1.50 % (1842706)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1842698"
% 0.18/1.50 % (1842708)Also succeeded, but the first one will report.
% 0.18/1.50 % (1842709)------------------------------
% 0.18/1.50 % (1842709)------------------------------
% 0.18/1.50 % (1842717)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2776617573:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.18/1.50 % (1842717)Also succeeded, but the first one will report.
% 0.18/1.50 % (1842706)Refutation found. Thanks to Tanya!
% 0.18/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.18/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.50 % (1842706)------------------------------
% 0.18/1.50 % (1842706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.50 % (1842706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.50 % (1842706)CaDiCaL version: 2.1.3
% 0.18/1.50 % (1842706)Termination reason: Refutation
% 0.18/1.50 % (1842706)Time elapsed: 0.005 s
% 0.18/1.50 % (1842706)Peak memory usage: 89 MB
% 0.18/1.50 % (1842706)Instructions burned: 6 (million)
% 0.18/1.50 % (1842706)------------------------------
% 0.18/1.50 % (1842706)------------------------------
% 0.18/1.50 % (1842698)Success in time 0.445 s
% 0.18/1.50 % Vampire exiting
%------------------------------------------------------------------------------