%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:42:01 PM UTC 2026
% Result : Unsatisfiable 6.02s 2.11s
% Output : Refutation 6.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 9 unt; 3 def)
% Number of atoms : 65 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 28 ~; 28 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 7 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f173,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
fof(f178,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
fof(f1434,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1435,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1436,negated_conjecture,
! [X0] :
( c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1437,negated_conjecture,
! [X0] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1463,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| 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)) ),
inference(resolution,[],[f178,f1436]) ).
fof(f1466,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(forward_subsumption_resolution,[],[f1463,f173]) ).
fof(f1472,definition,
( spl0_2
<=> v_n = v_m ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1474,plain,
( v_n = v_m
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1472]) ).
fof(f1477,definition,
( spl0_3
<=> c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f1478,plain,
( ~ c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| spl0_3 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f1479,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f1481,definition,
( spl0_4
<=> v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f1483,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f1481]) ).
fof(f1484,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f1466,f1481,f1477]) ).
fof(f1485,plain,
( v_n = v_m
| ~ spl0_3 ),
inference(resolution,[],[f1479,f178]) ).
fof(f1486,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1485,f1477,f1472]) ).
fof(f1490,plain,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),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_3 ),
inference(resolution,[],[f1478,f1437]) ).
fof(f1491,plain,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f1490,f173]) ).
fof(f1492,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))
| spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1491,f1483]) ).
fof(f1493,plain,
( $false
| spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1492,f173]) ).
fof(f1494,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f1493]) ).
fof(f1520,plain,
( ~ v_Q(v_n)
| ~ spl0_2 ),
inference(superposition,[],[f1435,f1474]) ).
fof(f1521,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1520,f1434]) ).
fof(f1522,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1521]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f1484]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f1486]) ).
cnf(s4,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f1494]) ).
cnf(s8,plain,
~ spl0_2,
inference(sat_conversion,[],[f1522]) ).
cnf(s9,plain,
~ spl0_3,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
~ spl0_4,
inference(rat,[],[s4,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s10,s9]) ).
fof(f1523,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n013.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 28 02:54:36 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.02/2.11 % (761991)Input is clausal, will run a generic CNF schedule.
% 6.02/2.11 % (761996)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=959584710:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.02/2.11 % (761998)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3097006307:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.02/2.11 % (761997)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4200534304:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.02/2.11 % (762002)dis-21_1_sil=8000:lcm=predicate:random_seed=2292602207: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)
% 6.02/2.11 % (761999)lrs+10_1_sil=8000:sp=occurrence:random_seed=1457888744:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.02/2.11 % (762000)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1790387029:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.02/2.11 % (762001)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1973732813:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.02/2.11 % (761999)Refutation not found, incomplete strategy
% 6.02/2.11 % (761999)------------------------------
% 6.02/2.11 % (761999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.02/2.11 % (761999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/2.11 % (761999)CaDiCaL version: 2.1.3
% 6.02/2.11 % (761999)Termination reason: Refutation not found, incomplete strategy
% 6.02/2.11 % (761999)Time elapsed: 0.006 s
% 6.02/2.11 % (761999)Peak memory usage: 88 MB
% 6.02/2.11 % (761999)Instructions burned: 4 (million)
% 6.02/2.11 % (762001)First to succeed.
% 6.02/2.11 % (762001)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-761991"
% 6.02/2.11 % (762002)Instruction limit reached!
% 6.02/2.11 % (762002)------------------------------
% 6.02/2.11 % (762002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.02/2.11 % (762002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/2.11 % (762002)CaDiCaL version: 2.1.3
% 6.02/2.11 % (762002)Termination reason: Instruction limit
% 6.02/2.11 % (762002)Termination phase: Saturation
% 6.02/2.11 % (762002)Time elapsed: 0.123 s
% 6.02/2.11 % (762002)Peak memory usage: 90 MB
% 6.02/2.11 % (762002)Instructions burned: 117 (million)
% 6.02/2.11 % (762000)Instruction limit reached!
% 6.02/2.11 % (762000)------------------------------
% 6.02/2.11 % (762000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.02/2.11 % (762000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/2.11 % (762000)CaDiCaL version: 2.1.3
% 6.02/2.11 % (762000)Termination reason: Instruction limit
% 6.02/2.11 % (762000)Termination phase: Saturation
% 6.02/2.11 % (762000)Time elapsed: 0.115 s
% 6.02/2.11 % (762000)Peak memory usage: 89 MB
% 6.02/2.11 % (762000)Instructions burned: 114 (million)
% 6.02/2.11 % (762012)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=2299141220:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 6.02/2.11 % (762012)Instruction limit reached!
% 6.02/2.11 % (762012)------------------------------
% 6.02/2.11 % (762012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.02/2.11 % (762012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/2.11 % (762012)CaDiCaL version: 2.1.3
% 6.02/2.11 % (762012)Termination reason: Instruction limit
% 6.02/2.11 % (762012)Termination phase: Saturation
% 6.02/2.11 % (762012)Time elapsed: 0.109 s
% 6.02/2.11 % (762012)Peak memory usage: 89 MB
% 6.02/2.11 % (762012)Instructions burned: 143 (million)
% 6.02/2.11 % (761999)------------------------------
% 6.02/2.11 % (761999)------------------------------
% 6.02/2.11 % (762013)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2251686924:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 6.02/2.11 % (762013)Refutation not found, incomplete strategy
% 6.02/2.11 % (762013)------------------------------
% 6.02/2.11 % (762013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.02/2.11 % (762013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/2.11 % (762013)CaDiCaL version: 2.1.3
% 6.02/2.11 % (762013)Termination reason: Refutation not found, incomplete strategy
% 6.02/2.11 % (762013)Time elapsed: 0.014 s
% 6.02/2.11 % (762013)Peak memory usage: 89 MB
% 6.02/2.11 % (762013)Instructions burned: 13 (million)
% 6.02/2.11 % (762001)Refutation found. Thanks to Tanya!
% 6.02/2.11 % SZS status Unsatisfiable for theBenchmark
% 6.02/2.11 % SZS output start Proof for theBenchmark
% See solution above
% 6.02/2.11 % (762001)------------------------------
% 6.02/2.11 % (762001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.02/2.11 % (762001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/2.11 % (762001)CaDiCaL version: 2.1.3
% 6.02/2.11 % (762001)Termination reason: Refutation
% 6.02/2.11 % (762001)Time elapsed: 0.025 s
% 6.02/2.11 % (762001)Peak memory usage: 90 MB
% 6.02/2.11 % (762001)Instructions burned: 23 (million)
% 6.02/2.11 % (762001)------------------------------
% 6.02/2.11 % (762001)------------------------------
% 6.02/2.11 % (761991)Success in time 0.748 s
% 6.02/2.11 % Vampire exiting
%------------------------------------------------------------------------------