%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET858-2 : 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 : n019.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 12:42:10 PM UTC 2026
% Result : Unsatisfiable 3.37s 1.35s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 76 ( 6 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 91 ( 37 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| c_lessequals(X3,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
fof(f6,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Zorn_Osucc(X1,c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X3,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| X0 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
fof(f12,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X1,X3,tc_set(tc_set(X2))) ),
inference(resolution,[],[f5,f6]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X0,X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2) = X3 ),
inference(resolution,[],[f10,f11]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X0,X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2) = X3 ),
inference(duplicate_literal_removal,[],[f35]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X0,X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2) = X3 ),
inference(forward_subsumption_resolution,[],[f36,f8]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X0,X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2) = X3 ),
inference(forward_subsumption_resolution,[],[f38,f7]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X0,X3,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(forward_subsumption_resolution,[],[f40,f9]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X0,X3,tc_set(tc_set(X2))) ),
inference(resolution,[],[f41,f12]) ).
fof(f177,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_m,X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f49,f1]) ).
fof(f242,plain,
( c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f177,f2]) ).
fof(f250,plain,
c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(forward_subsumption_resolution,[],[f242,f4]) ).
fof(f251,plain,
$false,
inference(forward_subsumption_resolution,[],[f250,f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:03:03 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.37/1.35 % (3623009)Input is clausal, will run a generic CNF schedule.
% 3.37/1.35 % (3623018)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1596100090:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.37/1.35 % (3623018)Instruction limit reached!
% 3.37/1.35 % (3623018)------------------------------
% 3.37/1.35 % (3623018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (3623018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (3623018)CaDiCaL version: 2.1.3
% 3.37/1.35 % (3623018)Termination reason: Instruction limit
% 3.37/1.35 % (3623018)Termination phase: Saturation
% 3.37/1.35 % (3623018)Time elapsed: 0.031 s
% 3.37/1.35 % (3623018)Peak memory usage: 87 MB
% 3.37/1.35 % (3623018)Instructions burned: 114 (million)
% 3.37/1.35 % (3623017)lrs+10_1_sil=8000:sp=occurrence:random_seed=2282023184:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.37/1.35 % (3623014)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=1596821100:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.37/1.35 % (3623015)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=557225594:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.37/1.35 % (3623016)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2024190283:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.37/1.35 % (3623019)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3363830369:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.37/1.35 % (3623017)First to succeed.
% 3.37/1.35 % (3623017)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3623009"
% 3.37/1.35 % (3623020)dis-21_1_sil=8000:lcm=predicate:random_seed=3174854519: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)
% 3.37/1.35 % (3623019)Also succeeded, but the first one will report.
% 3.37/1.35 % (3623023)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=2177068392:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.37/1.35 % (3623020)Instruction limit reached!
% 3.37/1.35 % (3623020)------------------------------
% 3.37/1.35 % (3623020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (3623020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (3623020)CaDiCaL version: 2.1.3
% 3.37/1.35 % (3623020)Termination reason: Instruction limit
% 3.37/1.35 % (3623020)Termination phase: Saturation
% 3.37/1.35 % (3623020)Time elapsed: 0.070 s
% 3.37/1.35 % (3623020)Peak memory usage: 89 MB
% 3.37/1.35 % (3623020)Instructions burned: 118 (million)
% 3.37/1.35 % (3623023)Refutation not found, incomplete strategy
% 3.37/1.35 % (3623023)------------------------------
% 3.37/1.35 % (3623023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (3623023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (3623023)CaDiCaL version: 2.1.3
% 3.37/1.35 % (3623023)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.35 % (3623023)Time elapsed: 0.001 s
% 3.37/1.35 % (3623023)Peak memory usage: 88 MB
% 3.37/1.35 % (3623023)Instructions burned: 1 (million)
% 3.37/1.35 % (3623030)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2544318567: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)
% 3.37/1.35 % (3623030)Also succeeded, but the first one will report.
% 3.37/1.35 % (3623023)------------------------------
% 3.37/1.35 % (3623023)------------------------------
% 3.37/1.35 % (3623017)Refutation found. Thanks to Tanya!
% 3.37/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.37/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.35 % (3623017)------------------------------
% 3.37/1.35 % (3623017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (3623017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (3623017)CaDiCaL version: 2.1.3
% 3.37/1.35 % (3623017)Termination reason: Refutation
% 3.37/1.35 % (3623017)Time elapsed: 0.015 s
% 3.37/1.35 % (3623017)Peak memory usage: 88 MB
% 3.37/1.35 % (3623017)Instructions burned: 21 (million)
% 3.37/1.35 % (3623017)------------------------------
% 3.37/1.35 % (3623017)------------------------------
% 3.37/1.35 % (3623009)Success in time 0.407 s
% 3.37/1.35 % Vampire exiting
%------------------------------------------------------------------------------