%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT023-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:36:45 PM UTC 2026
% Result : Unsatisfiable 3.57s 1.25s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 12 unt; 3 def)
% Number of atoms : 63 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 25 ~; 27 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f634,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Otrans(X3,X2)
| ~ c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__def_0) ).
fof(f640,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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f641,negated_conjecture,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f642,negated_conjecture,
! [X0] : ~ c_in(c_Pair(X0,X0,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f643,negated_conjecture,
~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f644,negated_conjecture,
! [X2,X0,X1] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f645,plain,
! [X2,X0,X1] :
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(reorient_equations,[],[f644]) ).
fof(f648,negated_conjecture,
! [X0,X1] :
( ~ c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X0,X1,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))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
fof(f674,plain,
( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_a = v_b ),
inference(resolution,[],[f645,f643]) ).
fof(f677,definition,
( spl0_1
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f679,plain,
( v_a = v_b
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f681,definition,
( spl0_2
<=> c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f683,plain,
( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f684,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f674,f681,f677]) ).
fof(f685,plain,
( c_in(c_Pair(v_b,v_a,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_a = v_b
| ~ spl0_2 ),
inference(resolution,[],[f683,f648]) ).
fof(f687,definition,
( spl0_3
<=> c_in(c_Pair(v_b,v_a,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_3])],[avatar_definition]) ).
fof(f689,plain,
( c_in(c_Pair(v_b,v_a,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))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f690,plain,
( spl0_1
| spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f685,f681,f687,f677]) ).
fof(f693,plain,
( c_in(c_Pair(v_a,v_a,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))
| ~ spl0_1 ),
inference(superposition,[],[f640,f679]) ).
fof(f694,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f693,f642]) ).
fof(f695,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f913,plain,
! [X2,X0,X1] :
( c_in(c_Pair(X2,X1,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(X2,X0,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(X0,X1,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)) ),
inference(resolution,[],[f634,f641]) ).
fof(f915,plain,
! [X0,X1] :
( ~ c_in(c_Pair(X0,X1,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(X1,X0,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)) ),
inference(resolution,[],[f913,f642]) ).
fof(f917,plain,
~ c_in(c_Pair(v_b,v_a,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)),
inference(resolution,[],[f915,f640]) ).
fof(f936,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f917,f689]) ).
fof(f937,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f936]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f684]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f690]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f695]) ).
cnf(s8,plain,
~ spl0_3,
inference(sat_conversion,[],[f937]) ).
cnf(s9,plain,
~ spl0_2,
inference(rat,[],[s2,s8,s3]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s3]) ).
fof(f938,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT023-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 23:31:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.57/1.25 % (1048567)Input is clausal, will run a generic CNF schedule.
% 3.57/1.25 % (1048575)lrs+10_1_sil=8000:sp=occurrence:random_seed=3572618327:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.57/1.25 % (1048573)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=929713468:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.57/1.25 % (1048576)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2479350874:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.57/1.25 % (1048574)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3627414486:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.57/1.25 % (1048572)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=3410345074:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.57/1.25 % (1048578)dis-21_1_sil=8000:lcm=predicate:random_seed=2374404549: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)
% 3.57/1.25 % (1048577)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3915833259:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.57/1.25 % (1048575)Instruction limit reached!
% 3.57/1.25 % (1048575)------------------------------
% 3.57/1.25 % (1048575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.25 % (1048575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.25 % (1048575)CaDiCaL version: 2.1.3
% 3.57/1.25 % (1048575)Termination reason: Instruction limit
% 3.57/1.25 % (1048575)Termination phase: Saturation
% 3.57/1.25 % (1048575)Time elapsed: 0.039 s
% 3.57/1.25 % (1048575)Peak memory usage: 90 MB
% 3.57/1.25 % (1048575)Instructions burned: 110 (million)
% 3.57/1.25 % (1048577)First to succeed.
% 3.57/1.25 % (1048577)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1048567"
% 3.57/1.25 % (1048578)Instruction limit reached!
% 3.57/1.25 % (1048578)------------------------------
% 3.57/1.25 % (1048578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.25 % (1048578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.25 % (1048578)CaDiCaL version: 2.1.3
% 3.57/1.25 % (1048578)Termination reason: Instruction limit
% 3.57/1.25 % (1048578)Termination phase: Saturation
% 3.57/1.25 % (1048578)Time elapsed: 0.070 s
% 3.57/1.25 % (1048578)Peak memory usage: 89 MB
% 3.57/1.25 % (1048578)Instructions burned: 117 (million)
% 3.57/1.25 % (1048576)Instruction limit reached!
% 3.57/1.25 % (1048576)------------------------------
% 3.57/1.25 % (1048576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.25 % (1048576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.25 % (1048576)CaDiCaL version: 2.1.3
% 3.57/1.25 % (1048576)Termination reason: Instruction limit
% 3.57/1.25 % (1048576)Termination phase: Saturation
% 3.57/1.25 % (1048576)Time elapsed: 0.076 s
% 3.57/1.25 % (1048576)Peak memory usage: 89 MB
% 3.57/1.25 % (1048576)Instructions burned: 114 (million)
% 3.57/1.25 % (1048586)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=1041832746:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.57/1.25 % (1048586)Also succeeded, but the first one will report.
% 3.57/1.25 % (1048587)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2227127920:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.57/1.25 % (1048588)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2877100751:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.57/1.25 % (1048577)Refutation found. Thanks to Tanya!
% 3.57/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.57/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.25 % (1048577)------------------------------
% 3.57/1.25 % (1048577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.25 % (1048577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.25 % (1048577)CaDiCaL version: 2.1.3
% 3.57/1.25 % (1048577)Termination reason: Refutation
% 3.57/1.25 % (1048577)Time elapsed: 0.031 s
% 3.57/1.25 % (1048577)Peak memory usage: 90 MB
% 3.57/1.25 % (1048577)Instructions burned: 46 (million)
% 3.57/1.25 % (1048577)------------------------------
% 3.57/1.25 % (1048577)------------------------------
% 3.57/1.25 % (1048567)Success in time 0.461 s
% 3.57/1.25 % Vampire exiting
%------------------------------------------------------------------------------