TSTP Solution File: SET825-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET825-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:19:04 EDT 2024
% Result : Unsatisfiable 2.24s 0.64s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 60 ( 14 unt; 0 def)
% Number of atoms : 115 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 101 ( 46 ~; 48 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8666,plain,
$false,
inference(avatar_sat_refutation,[],[f2521,f2526,f2563,f5180,f8504,f8652,f8665]) ).
fof(f8665,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f8664]) ).
fof(f8664,plain,
( $false
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f8663,f1358]) ).
fof(f1358,axiom,
v_Q(v_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f8663,plain,
( ~ v_Q(v_n)
| ~ spl0_7 ),
inference(superposition,[],[f1359,f8654]) ).
fof(f8654,plain,
( v_n = v_m
| ~ spl0_7 ),
inference(resolution,[],[f8503,f131]) ).
fof(f131,axiom,
! [X2,X6,X4] :
( ~ c_in(c_Pair(X4,X6,X2,X2),c_Relation_OId,tc_prod(X2,X2))
| X4 = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
fof(f8503,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f8501]) ).
fof(f8501,plain,
( spl0_7
<=> c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1359,axiom,
~ v_Q(v_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f8652,plain,
( ~ spl0_6
| spl0_7 ),
inference(avatar_contradiction_clause,[],[f8651]) ).
fof(f8651,plain,
( $false
| ~ spl0_6
| spl0_7 ),
inference(subsumption_resolution,[],[f8650,f126]) ).
fof(f126,axiom,
! [X2,X4] : c_in(c_Pair(X4,X4,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
fof(f8650,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_6
| spl0_7 ),
inference(subsumption_resolution,[],[f8649,f8502]) ).
fof(f8502,plain,
( ~ c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| spl0_7 ),
inference(avatar_component_clause,[],[f8501]) ).
fof(f8649,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f8641,f126]) ).
fof(f8641,plain,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_6 ),
inference(superposition,[],[f1361,f8499]) ).
fof(f8499,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f8497]) ).
fof(f8497,plain,
( spl0_6
<=> v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1361,axiom,
! [X41] :
( ~ c_in(c_Pair(c_Suc(v_x(X41)),c_Suc(v_xa(X41)),tc_nat,tc_nat),X41,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X41,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X41,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8504,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f8494,f8501,f8497]) ).
fof(f8494,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
inference(subsumption_resolution,[],[f8456,f126]) ).
fof(f8456,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
inference(resolution,[],[f1360,f131]) ).
fof(f1360,axiom,
! [X41] :
( c_in(c_Pair(v_x(X41),v_xa(X41),tc_nat,tc_nat),X41,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X41,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X41,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5180,plain,
( ~ spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f4951,f2519,f5177]) ).
fof(f5177,plain,
( spl0_5
<=> c_0 = c_Divides_Oop_Amod(c_uminus(c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f2519,plain,
( spl0_2
<=> ! [X0] : c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f4951,plain,
! [X0] :
( c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_uminus(c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(resolution,[],[f2452,f2410]) ).
fof(f2410,plain,
! [X0] : c_Divides_Oop_Advd(c_uminus(c_uminus(c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),X0,tc_IntDef_Oint),
inference(resolution,[],[f2406,f1983]) ).
fof(f1983,plain,
! [X0,X1] :
( ~ c_Divides_Oop_Advd(X0,c_uminus(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
inference(resolution,[],[f1765,f45]) ).
fof(f45,axiom,
! [X19,X20] :
( ~ c_Divides_Oop_Advd(X19,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
fof(f1765,plain,
! [X0,X1] :
( c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[],[f50,f45]) ).
fof(f50,axiom,
! [X19,X20] :
( c_Divides_Oop_Advd(c_uminus(X19,tc_IntDef_Oint),X20,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
fof(f2406,plain,
! [X0] : c_Divides_Oop_Advd(c_uminus(c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),X0,tc_IntDef_Oint),
inference(resolution,[],[f2402,f1983]) ).
fof(f2402,plain,
! [X0] : c_Divides_Oop_Advd(c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),X0,tc_IntDef_Oint),
inference(resolution,[],[f2394,f1983]) ).
fof(f2394,plain,
! [X0] : c_Divides_Oop_Advd(c_uminus(c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint),
inference(resolution,[],[f1983,f238]) ).
fof(f238,axiom,
! [X12] : c_Divides_Oop_Advd(c_1,X12,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f2452,plain,
! [X0,X1] :
( ~ c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(X0,c_0,tc_IntDef_Oint) ),
inference(superposition,[],[f50,f2418]) ).
fof(f2418,plain,
! [X0] :
( c_0 = c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(X0,c_0,tc_IntDef_Oint) ),
inference(resolution,[],[f2415,f1732]) ).
fof(f1732,plain,
! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) ),
inference(resolution,[],[f46,f47]) ).
fof(f47,axiom,
! [X12] :
( ~ c_Divides_Oop_Advd(c_0,X12,tc_IntDef_Oint)
| c_0 = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
fof(f46,axiom,
! [X19,X20] :
( c_Divides_Oop_Advd(X19,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
fof(f2415,plain,
! [X0] :
( c_Divides_Oop_Advd(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(X0,c_0,tc_IntDef_Oint) ),
inference(superposition,[],[f2219,f1734]) ).
fof(f1734,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(resolution,[],[f1732,f48]) ).
fof(f48,axiom,
c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).
fof(f2219,plain,
! [X0,X1] :
( c_0 != c_Divides_Oop_Amod(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(superposition,[],[f1933,f241]) ).
fof(f241,axiom,
! [X39,X12] :
( c_times(X39,c_Main_Ozmod__eq__0D__dest__1(X39,X12),tc_IntDef_Oint) = X12
| c_0 != c_Divides_Oop_Amod(X12,X39,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f1933,plain,
! [X0,X1] : c_Divides_Oop_Advd(X0,c_uminus(c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolution,[],[f1742,f239]) ).
fof(f239,axiom,
! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f1742,plain,
! [X0,X1] :
( ~ c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[],[f49,f46]) ).
fof(f49,axiom,
! [X19,X20] :
( ~ c_Divides_Oop_Advd(c_uminus(X19,tc_IntDef_Oint),X20,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
fof(f2563,plain,
( ~ spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f2445,f2519,f2560]) ).
fof(f2560,plain,
( spl0_4
<=> c_0 = c_Divides_Oop_Amod(c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f2445,plain,
! [X0] :
( c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(superposition,[],[f2410,f2418]) ).
fof(f2526,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f2444,f2519,f2523]) ).
fof(f2523,plain,
( spl0_3
<=> c_0 = c_Divides_Oop_Amod(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f2444,plain,
! [X0] :
( c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(superposition,[],[f2406,f2418]) ).
fof(f2521,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f2448,f2519,f2515]) ).
fof(f2515,plain,
( spl0_1
<=> c_0 = c_Divides_Oop_Amod(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f2448,plain,
! [X0] :
( c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_1,c_0,tc_IntDef_Oint) ),
inference(superposition,[],[f2402,f2418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET825-1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.29 % Computer : n010.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri May 3 16:58:37 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % (31591)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.33 % (31594)WARNING: value z3 for option sas not known
% 0.14/0.34 % (31593)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.34 % (31594)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.34 % (31598)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.34 % (31595)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.34 % (31592)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.34 % (31596)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.34 % (31597)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.49 TRYING [1]
% 0.14/0.50 TRYING [2]
% 0.14/0.51 TRYING [3]
% 1.55/0.57 TRYING [3]
% 1.55/0.62 TRYING [1]
% 2.24/0.64 % (31594)First to succeed.
% 2.24/0.64 % (31594)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31591"
% 2.24/0.64 % (31594)Refutation found. Thanks to Tanya!
% 2.24/0.64 % SZS status Unsatisfiable for theBenchmark
% 2.24/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.24/0.64 % (31594)------------------------------
% 2.24/0.64 % (31594)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.24/0.64 % (31594)Termination reason: Refutation
% 2.24/0.64
% 2.24/0.64 % (31594)Memory used [KB]: 5765
% 2.24/0.64 % (31594)Time elapsed: 0.302 s
% 2.24/0.64 % (31594)Instructions burned: 648 (million)
% 2.24/0.64 % (31591)Success in time 0.332 s
%------------------------------------------------------------------------------