%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT070-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:36:51 PM UTC 2026
% Result : Unsatisfiable 2.68s 1.37s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 43 ( 6 unt; 4 def)
% Number of atoms : 130 ( 18 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 146 ( 59 ~; 83 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f737,axiom,
( v_b____ != v_a_H____
| v_a____ != v_b_H____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f738,axiom,
( v_b____ != v_a_H____
| v_a____ != v_b_H____
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f739,axiom,
( v_b____ != v_a_H____
| v_a____ = v_b_H____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1_01) ).
fof(f740,axiom,
( v_b____ != v_a_H____
| v_a____ = v_b_H____
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
fof(f741,axiom,
( v_a____ != v_b_H____
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1_03) ).
fof(f742,axiom,
( v_a____ != v_b_H____
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_04) ).
fof(f743,axiom,
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a_H____
| v_a____ = v_b_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1_05) ).
fof(f744,axiom,
( c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_b____ = v_a_H____
| v_a____ = v_b_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_06) ).
fof(f745,negated_conjecture,
( ~ c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f746,negated_conjecture,
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f770,definition,
( spl0_1
<=> c_in(c_Pair(v_a_H____,v_b_H____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P_H____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f774,definition,
( spl0_2
<=> c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P____),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f778,definition,
( spl0_3
<=> v_a____ = v_b_H____ ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f782,definition,
( spl0_4
<=> v_b____ = v_a_H____ ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f785,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f737,f782,f778,f774,f770]) ).
fof(f786,plain,
( ~ spl0_2
| spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f738,f782,f778,f770,f774]) ).
fof(f787,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f739,f782,f778,f774,f770]) ).
fof(f788,plain,
( ~ spl0_2
| spl0_1
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f740,f782,f778,f770,f774]) ).
fof(f789,plain,
( spl0_4
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f741,f778,f774,f770,f782]) ).
fof(f790,plain,
( spl0_4
| ~ spl0_2
| spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f742,f778,f770,f774,f782]) ).
fof(f791,plain,
( spl0_3
| spl0_4
| ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f743,f774,f770,f782,f778]) ).
fof(f792,plain,
( spl0_3
| spl0_4
| ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f744,f770,f774,f782,f778]) ).
fof(f793,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f746,f774,f770]) ).
fof(f794,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f745,f770,f774]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f785]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f786]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f787]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f788]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f789]) ).
cnf(s6,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f790]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f791]) ).
cnf(s8,plain,
( spl0_1
| ~ spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f792]) ).
cnf(s9,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f793]) ).
cnf(s10,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f794]) ).
cnf(s11,plain,
( spl0_3
| ~ spl0_2
| spl0_1 ),
inference(rat,[],[s8,s4]) ).
cnf(s12,plain,
( ~ spl0_3
| ~ spl0_2
| spl0_1 ),
inference(rat,[],[s2,s6]) ).
cnf(s13,plain,
( ~ spl0_2
| spl0_1 ),
inference(rat,[],[s12,s11]) ).
cnf(s14,plain,
spl0_1,
inference(rat,[],[s13,s9]) ).
cnf(s15,plain,
~ spl0_2,
inference(rat,[],[s10,s14]) ).
cnf(s16,plain,
spl0_3,
inference(rat,[],[s7,s3,s14,s15]) ).
cnf(s17,plain,
spl0_4,
inference(rat,[],[s5,s15,s14,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s15,s14,s17,s16]) ).
fof(f795,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT070-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 23:39:09 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.68/1.37 % (2855127)Input is clausal, will run a generic CNF schedule.
% 2.68/1.37 % (2855135)lrs+10_1_sil=8000:sp=occurrence:random_seed=659157962:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.68/1.37 % (2855135)First to succeed.
% 2.68/1.37 % (2855135)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2855127"
% 2.68/1.37 % (2855132)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=2511280976:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.68/1.37 % (2855138)dis-21_1_sil=8000:lcm=predicate:random_seed=3824940286: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)
% 2.68/1.37 % (2855137)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1229151375:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.68/1.37 % (2855134)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3877323352:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.68/1.37 % (2855136)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1303533332:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.68/1.37 % (2855133)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4001141706:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.68/1.37 % (2855136)Also succeeded, but the first one will report.
% 2.68/1.37 % (2855137)Also succeeded, but the first one will report.
% 2.68/1.37 % (2855138)Also succeeded, but the first one will report.
% 2.68/1.37 % (2855135)Refutation found. Thanks to Tanya!
% 2.68/1.37 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.37 % (2855135)------------------------------
% 2.68/1.37 % (2855135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.37 % (2855135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.37 % (2855135)CaDiCaL version: 2.1.3
% 2.68/1.37 % (2855135)Termination reason: Refutation
% 2.68/1.37 % (2855135)Time elapsed: 0.003 s
% 2.68/1.37 % (2855135)Peak memory usage: 89 MB
% 2.68/1.37 % (2855135)Instructions burned: 4 (million)
% 2.68/1.37 % (2855135)------------------------------
% 2.68/1.37 % (2855135)------------------------------
% 2.68/1.37 % (2855127)Success in time 0.322 s
% 2.68/1.37 % Vampire exiting
%------------------------------------------------------------------------------