%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT126+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 : n010.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 4.74s 1.67s
% Output : Refutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 42 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 45 ( 23 ~; 12 |; 4 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
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))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Q_A_058_AProf_096) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( X3 = X2
=> ( ( hBOOL(hAPP(hAPP(c_member(X1),X0),X3))
=> ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X3))
=> hBOOL(hAPP(hAPP(c_member(X1),X0),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
fof(f24,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,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_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(f37,axiom,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X3),c_FuncSet_OPi(X5,X4,X2,X1)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X0)),hAPP(X1,X0)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
fof(f514,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(f525,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f526,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(negated_conjecture,[status(cth)],[f525]) ).
fof(f527,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(flattening,[],[f526]) ).
fof(f553,plain,
! [X0,X1,X2,X3] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
& ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X3)) )
| ( hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
& hBOOL(hAPP(hAPP(c_member(X1),X0),X3)) )
| X2 != X3 ),
inference(ennf_transformation,[],[f7]) ).
fof(f554,plain,
! [X0,X1,X2,X3] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
& ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X3)) )
| ( hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
& hBOOL(hAPP(hAPP(c_member(X1),X0),X3)) )
| X2 != X3 ),
inference(flattening,[],[f553]) ).
fof(f575,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X2))
| hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X0)),hAPP(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X3),c_FuncSet_OPi(X5,X4,X2,X1))) ),
inference(ennf_transformation,[],[f37]) ).
fof(f576,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X2))
| hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X0)),hAPP(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X3),c_FuncSet_OPi(X5,X4,X2,X1))) ),
inference(flattening,[],[f575]) ).
fof(f1190,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))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f4]) ).
fof(f1194,plain,
! [X2,X3,X0,X1] :
( X2 != X3
| hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X3)) ),
inference(cnf_transformation,[],[f554]) ).
fof(f1242,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,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_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(cnf_transformation,[],[f24]) ).
fof(f1273,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X3),c_FuncSet_OPi(X5,X4,X2,X1)))
| hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X0)),hAPP(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X2)) ),
inference(cnf_transformation,[],[f576]) ).
fof(f1915,plain,
! [X2,X3,X0,X1] : hAPP(c_COMBK(X3,X2,X1),X0) = X1,
inference(cnf_transformation,[],[f514]) ).
fof(f1926,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f527]) ).
fof(f2015,plain,
! [X2,X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(c_COMBK(X0,X1,c_Arrow__Order__Mirabelle_OLin),X2))),
inference(unit_resulting_resolution,[],[f1194,f1926,f1915]) ).
fof(f2704,plain,
$false,
inference(unit_resulting_resolution,[],[f1273,f1190,f2015,f1242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT126+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:46:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 4.74/1.67 % (1430301)Detected formulas, will run a generic FOF schedule.
% 4.74/1.67 % (1430309)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1933667711:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.74/1.67 % (1430309)Refutation not found, incomplete strategy
% 4.74/1.67 % (1430309)------------------------------
% 4.74/1.67 % (1430309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.67 % (1430309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.67 % (1430309)CaDiCaL version: 2.1.3
% 4.74/1.67 % (1430309)Termination reason: Refutation not found, incomplete strategy
% 4.74/1.67 % (1430309)Time elapsed: 0.002 s
% 4.74/1.67 % (1430309)Peak memory usage: 89 MB
% 4.74/1.67 % (1430309)Instructions burned: 4 (million)
% 4.74/1.67 % (1430310)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2846920744:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.74/1.67 % (1430308)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=4249512965:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.74/1.67 % (1430307)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=1740591334:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.74/1.67 % (1430312)dis-21_1_sil=8000:lcm=predicate:random_seed=3096535894: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)
% 4.74/1.67 % (1430306)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=1949701858:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.74/1.67 % (1430311)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=540488591:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.74/1.67 % (1430312)Instruction limit reached!
% 4.74/1.67 % (1430312)------------------------------
% 4.74/1.67 % (1430312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.67 % (1430312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.67 % (1430312)CaDiCaL version: 2.1.3
% 4.74/1.67 % (1430312)Termination reason: Instruction limit
% 4.74/1.67 % (1430312)Termination phase: Saturation
% 4.74/1.67 % (1430312)Time elapsed: 0.066 s
% 4.74/1.67 % (1430312)Peak memory usage: 89 MB
% 4.74/1.67 % (1430312)Instructions burned: 129 (million)
% 4.74/1.67 % (1430310)Instruction limit reached!
% 4.74/1.67 % (1430310)------------------------------
% 4.74/1.67 % (1430310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.67 % (1430310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.67 % (1430310)CaDiCaL version: 2.1.3
% 4.74/1.67 % (1430310)Termination reason: Instruction limit
% 4.74/1.67 % (1430310)Termination phase: Saturation
% 4.74/1.67 % (1430310)Time elapsed: 0.072 s
% 4.74/1.67 % (1430310)Peak memory usage: 89 MB
% 4.74/1.67 % (1430310)Instructions burned: 121 (million)
% 4.74/1.67 % (1430311)Instruction limit reached!
% 4.74/1.67 % (1430311)------------------------------
% 4.74/1.67 % (1430311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.67 % (1430311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.67 % (1430311)CaDiCaL version: 2.1.3
% 4.74/1.67 % (1430311)Termination reason: Instruction limit
% 4.74/1.67 % (1430311)Termination phase: Saturation
% 4.74/1.67 % (1430311)Time elapsed: 0.076 s
% 4.74/1.67 % (1430311)Peak memory usage: 90 MB
% 4.74/1.67 % (1430311)Instructions burned: 140 (million)
% 4.74/1.67 % (1430309)------------------------------
% 4.74/1.67 % (1430309)------------------------------
% 4.74/1.67 % (1430320)lrs+10_1_sil=8000:sp=occurrence:random_seed=2627492535:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.74/1.67 % (1430323)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3907199400:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.74/1.67 % (1430322)lrs+1011_1_sil=32000:sp=occurrence:random_seed=959544364:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.74/1.67 % (1430321)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2587893363:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.74/1.67 % (1430323)First to succeed.
% 4.74/1.67 % (1430323)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1430301"
% 4.74/1.67 % (1430321)Instruction limit reached!
% 4.74/1.67 % (1430321)------------------------------
% 4.74/1.67 % (1430321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.67 % (1430321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.67 % (1430321)CaDiCaL version: 2.1.3
% 4.74/1.67 % (1430321)Termination reason: Instruction limit
% 4.74/1.67 % (1430321)Termination phase: Saturation
% 4.74/1.67 % (1430321)Time elapsed: 0.083 s
% 4.74/1.67 % (1430321)Peak memory usage: 89 MB
% 4.74/1.67 % (1430321)Instructions burned: 157 (million)
% 4.74/1.67 % (1430320)Instruction limit reached!
% 4.74/1.67 % (1430320)------------------------------
% 4.74/1.67 % (1430320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.67 % (1430320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.67 % (1430320)CaDiCaL version: 2.1.3
% 4.74/1.67 % (1430320)Termination reason: Instruction limit
% 4.74/1.67 % (1430320)Termination phase: Saturation
% 4.74/1.67 % (1430320)Time elapsed: 0.180 s
% 4.74/1.67 % (1430320)Peak memory usage: 92 MB
% 4.74/1.67 % (1430320)Instructions burned: 286 (million)
% 4.74/1.67 % (1430323)Refutation found. Thanks to Tanya!
% 4.74/1.67 % SZS status Theorem for theBenchmark
% 4.74/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 4.74/1.67 % (1430323)------------------------------
% 4.74/1.67 % (1430323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.67 % (1430323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.67 % (1430323)CaDiCaL version: 2.1.3
% 4.74/1.67 % (1430323)Termination reason: Refutation
% 4.74/1.67 % (1430323)Time elapsed: 0.028 s
% 4.74/1.67 % (1430323)Peak memory usage: 90 MB
% 4.74/1.67 % (1430323)Instructions burned: 94 (million)
% 4.74/1.67 % (1430323)------------------------------
% 4.74/1.67 % (1430323)------------------------------
% 4.74/1.67 % (1430301)Success in time 0.613 s
% 4.74/1.67 % Vampire exiting
%------------------------------------------------------------------------------