%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT123+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:36:58 PM UTC 2026
% Result : Theorem 3.39s 1.39s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 14 unt; 0 def)
% Number of atoms : 25 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-5 aty)
% Number of variables : 30 ( 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f110,axiom,
c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Prof__def) ).
fof(f112,axiom,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X4),X5),X3))
=> hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,X5)),X0)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),X1),c_FuncSet_OPi(X4,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(f520,axiom,
! [X0,X1,X2,X3] : hAPP(c_COMBK(X3,X2,X1),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(f528,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f529,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f530,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
inference(negated_conjecture,[status(cth)],[f529]) ).
fof(f531,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
inference(flattening,[],[f530]) ).
fof(f544,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),X1),c_FuncSet_OPi(X4,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0))))
| ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,X5)),X0))
& hBOOL(hAPP(hAPP(c_member(X4),X5),X3)) ) ),
inference(ennf_transformation,[],[f112]) ).
fof(f553,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),X1),c_FuncSet_OPi(X4,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0))))
| ( ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,sK1(X0,X1,X2,X3,X4))),X0))
& hBOOL(hAPP(hAPP(c_member(X4),sK1(X0,X1,X2,X3,X4)),X3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X5,sK1(X0,X1,X2,X3,X4))],[f544]) ).
fof(f554,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f528]) ).
fof(f555,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f531]) ).
fof(f573,plain,
c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f110]) ).
fof(f574,plain,
! [X2,X3,X0,X1] : hAPP(c_COMBK(X3,X2,X1),X0) = X1,
inference(cnf_transformation,[],[f520]) ).
fof(f581,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),X1),c_FuncSet_OPi(X4,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0))))
| ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X1,sK1(X0,X1,X2,X3,X4))),X0)) ),
inference(cnf_transformation,[],[f553]) ).
fof(f595,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L)),c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_OLin)))),
inference(forward_demodulation,[],[f555,f573]) ).
fof(f597,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L),sK1(c_Arrow__Order__Mirabelle_OLin,c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,v_L),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
inference(resolution,[],[f595,f581]) ).
fof(f599,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_L),c_Arrow__Order__Mirabelle_OLin)),
inference(forward_demodulation,[],[f597,f574]) ).
fof(f600,plain,
$false,
inference(forward_subsumption_resolution,[],[f599,f554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT123+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 23:47:54 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.39/1.39 % (2859668)Detected formulas, will run a generic FOF schedule.
% 3.39/1.39 % (2859673)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=3708090955:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/1.39 % (2859678)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3322393722:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/1.39 % (2859675)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3150355010:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/1.39 % (2859677)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3933895360:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/1.39 % (2859676)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2007046872:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/1.39 % (2859679)dis-21_1_sil=8000:lcm=predicate:random_seed=3923970175:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.39/1.39 % (2859674)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1619850868:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/1.39 % (2859676)First to succeed.
% 3.39/1.39 % (2859676)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2859668"
% 3.39/1.39 % (2859678)Instruction limit reached!
% 3.39/1.39 % (2859678)------------------------------
% 3.39/1.39 % (2859678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.39 % (2859678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.39 % (2859678)CaDiCaL version: 2.1.3
% 3.39/1.39 % (2859678)Termination reason: Instruction limit
% 3.39/1.39 % (2859678)Termination phase: Saturation
% 3.39/1.39 % (2859678)Time elapsed: 0.039 s
% 3.39/1.39 % (2859678)Peak memory usage: 90 MB
% 3.39/1.39 % (2859678)Instructions burned: 139 (million)
% 3.39/1.39 % (2859679)Instruction limit reached!
% 3.39/1.39 % (2859679)------------------------------
% 3.39/1.39 % (2859679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.39 % (2859679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.39 % (2859679)CaDiCaL version: 2.1.3
% 3.39/1.39 % (2859679)Termination reason: Instruction limit
% 3.39/1.39 % (2859679)Termination phase: Saturation
% 3.39/1.39 % (2859679)Time elapsed: 0.069 s
% 3.39/1.39 % (2859679)Peak memory usage: 90 MB
% 3.39/1.39 % (2859679)Instructions burned: 129 (million)
% 3.39/1.39 % (2859677)Instruction limit reached!
% 3.39/1.39 % (2859677)------------------------------
% 3.39/1.39 % (2859677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.39 % (2859677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.39 % (2859677)CaDiCaL version: 2.1.3
% 3.39/1.39 % (2859677)Termination reason: Instruction limit
% 3.39/1.39 % (2859677)Termination phase: Saturation
% 3.39/1.39 % (2859677)Time elapsed: 0.070 s
% 3.39/1.39 % (2859677)Peak memory usage: 89 MB
% 3.39/1.39 % (2859677)Instructions burned: 119 (million)
% 3.39/1.39 % (2859687)lrs+10_1_sil=8000:sp=occurrence:random_seed=2605628207:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.39/1.39 % (2859688)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3100513957:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.39/1.39 % (2859689)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4167675364:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.39/1.39 % (2859687)Instruction limit reached!
% 3.39/1.39 % (2859687)------------------------------
% 3.39/1.39 % (2859687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.39 % (2859687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.39 % (2859687)CaDiCaL version: 2.1.3
% 3.39/1.39 % (2859687)Termination reason: Instruction limit
% 3.39/1.39 % (2859687)Termination phase: Saturation
% 3.39/1.39 % (2859687)Time elapsed: 0.095 s
% 3.39/1.39 % (2859687)Peak memory usage: 92 MB
% 3.39/1.39 % (2859687)Instructions burned: 287 (million)
% 3.39/1.39 % (2859688)Also succeeded, but the first one will report.
% 3.39/1.39 % (2859676)Refutation found. Thanks to Tanya!
% 3.39/1.39 % SZS status Theorem for theBenchmark
% 3.39/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.39 % (2859676)------------------------------
% 3.39/1.39 % (2859676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.39 % (2859676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.39 % (2859676)CaDiCaL version: 2.1.3
% 3.39/1.39 % (2859676)Termination reason: Refutation
% 3.39/1.39 % (2859676)Time elapsed: 0.006 s
% 3.39/1.39 % (2859676)Peak memory usage: 89 MB
% 3.39/1.39 % (2859676)Instructions burned: 7 (million)
% 3.39/1.39 % (2859676)------------------------------
% 3.39/1.39 % (2859676)------------------------------
% 3.39/1.39 % (2859668)Success in time 0.447 s
% 3.39/1.39 % Vampire exiting
%------------------------------------------------------------------------------