%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW299+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 : n014.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 01:30:03 PM UTC 2026
% Result : Theorem 4.27s 1.73s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 9 unt; 1 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 78 ( 32 ~; 28 |; 8 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 42 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5222,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5223,axiom,
! [X0,X1] :
( v_P(X0,X1)
=> ! [X2] :
( ! [X3] :
( hBOOL(hAPP(hAPP(v_P_H,X3),X1))
=> hBOOL(hAPP(hAPP(v_Q_H,X3),X2)) )
=> v_Q(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5224,conjecture,
! [X0,X1] :
( v_P(X0,X1)
=> ? [X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
& ! [X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(X2,X5),X1))
=> hBOOL(hAPP(hAPP(X3,X5),X4)) )
=> v_Q(X0,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f5225,negated_conjecture,
~ ! [X0,X1] :
( v_P(X0,X1)
=> ? [X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
& ! [X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(X2,X5),X1))
=> hBOOL(hAPP(hAPP(X3,X5),X4)) )
=> v_Q(X0,X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f5224]) ).
fof(f5227,plain,
! [X0,X1] :
( ! [X2] :
( v_Q(X0,X2)
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,X3),X2))
& hBOOL(hAPP(hAPP(v_P_H,X3),X1)) ) )
| ~ v_P(X0,X1) ),
inference(ennf_transformation,[],[f5223]) ).
fof(f5228,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| ? [X4] :
( ~ v_Q(X0,X4)
& ! [X5] :
( hBOOL(hAPP(hAPP(X3,X5),X4))
| ~ hBOOL(hAPP(hAPP(X2,X5),X1)) ) ) )
& v_P(X0,X1) ),
inference(ennf_transformation,[],[f5225]) ).
fof(f5274,plain,
! [X0,X1] :
( ! [X2] :
( v_Q(X0,X2)
| ( ~ hBOOL(hAPP(hAPP(v_Q_H,sK1(X1,X2)),X2))
& hBOOL(hAPP(hAPP(v_P_H,sK1(X1,X2)),X1)) ) )
| ~ v_P(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X1,X2))],[f5227]) ).
fof(f5275,plain,
( ! [X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| ( ~ v_Q(sK2,sK4(X2,X3))
& ! [X5] :
( hBOOL(hAPP(hAPP(X3,X5),sK4(X2,X3)))
| ~ hBOOL(hAPP(hAPP(X2,X5),sK3)) ) ) )
& v_P(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X4,sK4(X2,X3))],[f5228]) ).
fof(f5312,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5222]) ).
fof(f5313,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(v_P_H,sK1(X1,X2)),X1))
| v_Q(X0,X2)
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[],[f5274]) ).
fof(f5314,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,sK1(X1,X2)),X2))
| v_Q(X0,X2)
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[],[f5274]) ).
fof(f5315,plain,
v_P(sK2,sK3),
inference(cnf_transformation,[],[f5275]) ).
fof(f5316,plain,
! [X2,X3,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(X3,X5),sK4(X2,X3)))
| ~ hBOOL(hAPP(hAPP(X2,X5),sK3)) ),
inference(cnf_transformation,[],[f5275]) ).
fof(f5317,plain,
! [X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| ~ v_Q(sK2,sK4(X2,X3)) ),
inference(cnf_transformation,[],[f5275]) ).
fof(f5472,plain,
! [X0] :
( hBOOL(hAPP(hAPP(v_Q_H,X0),sK4(v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,X0),sK3)) ),
inference(resolution,[],[f5312,f5316]) ).
fof(f5473,plain,
~ v_Q(sK2,sK4(v_P_H,v_Q_H)),
inference(resolution,[],[f5312,f5317]) ).
fof(f5479,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P_H,sK1(X0,sK4(v_P_H,v_Q_H))),sK3))
| v_Q(X1,sK4(v_P_H,v_Q_H))
| ~ v_P(X1,X0) ),
inference(resolution,[],[f5472,f5314]) ).
fof(f5516,plain,
! [X0,X1] :
( v_Q(X0,sK4(v_P_H,v_Q_H))
| ~ v_P(X0,sK3)
| v_Q(X1,sK4(v_P_H,v_Q_H))
| ~ v_P(X1,sK3) ),
inference(resolution,[],[f5479,f5313]) ).
fof(f5527,definition,
( spl17_7
<=> ! [X1] :
( v_Q(X1,sK4(v_P_H,v_Q_H))
| ~ v_P(X1,sK3) ) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
fof(f5528,plain,
( ! [X1] :
( v_Q(X1,sK4(v_P_H,v_Q_H))
| ~ v_P(X1,sK3) )
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f5527]) ).
fof(f5529,plain,
( spl17_7
| spl17_7 ),
inference(avatar_split_clause,[],[f5516,f5527,f5527]) ).
fof(f5562,plain,
( ~ v_P(sK2,sK3)
| ~ spl17_7 ),
inference(resolution,[],[f5528,f5473]) ).
fof(f5563,plain,
( $false
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f5562,f5315]) ).
fof(f5564,plain,
~ spl17_7,
inference(avatar_contradiction_clause,[],[f5563]) ).
cnf(s6,plain,
( spl17_7
| spl17_7 ),
inference(sat_conversion,[],[f5529]) ).
cnf(s7,plain,
spl17_7,
inference(rat,[],[s6]) ).
cnf(s9,plain,
~ spl17_7,
inference(sat_conversion,[],[f5564]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s7,s9]) ).
fof(f5565,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW299+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n014.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 13:31:01 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 4.27/1.73 % (1777288)Detected formulas, will run a generic FOF schedule.
% 4.27/1.73 % (1777293)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=947402956:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 4.27/1.73 % (1777299)dis-21_1_sil=8000:lcm=predicate:random_seed=3374200138:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2995 on theBenchmark for (2995ds/129Mi)
% 4.27/1.73 % (1777294)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=207573792:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 4.27/1.73 % (1777298)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1148083715:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 4.27/1.73 % (1777297)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=226488280:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 4.27/1.73 % (1777296)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2794276393:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 4.27/1.73 % (1777295)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=738753043:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 4.27/1.73 % (1777296)First to succeed.
% 4.27/1.73 % (1777296)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1777288"
% 4.27/1.73 % (1777298)Instruction limit reached!
% 4.27/1.73 % (1777298)------------------------------
% 4.27/1.73 % (1777298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.73 % (1777298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.73 % (1777298)CaDiCaL version: 2.1.3
% 4.27/1.73 % (1777298)Termination reason: Instruction limit
% 4.27/1.73 % (1777298)Termination phase: SInE selection
% 4.27/1.73 % (1777298)Time elapsed: 0.057 s
% 4.27/1.73 % (1777298)Peak memory usage: 90 MB
% 4.27/1.73 % (1777298)Instructions burned: 139 (million)
% 4.27/1.73 % (1777297)Instruction limit reached!
% 4.27/1.73 % (1777297)------------------------------
% 4.27/1.73 % (1777297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.73 % (1777297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.73 % (1777297)CaDiCaL version: 2.1.3
% 4.27/1.73 % (1777297)Termination reason: Instruction limit
% 4.27/1.73 % (1777297)Termination phase: Saturation
% 4.27/1.73 % (1777297)Time elapsed: 0.065 s
% 4.27/1.73 % (1777297)Peak memory usage: 94 MB
% 4.27/1.73 % (1777297)Instructions burned: 119 (million)
% 4.27/1.73 % (1777299)Instruction limit reached!
% 4.27/1.73 % (1777299)------------------------------
% 4.27/1.73 % (1777299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.73 % (1777299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.73 % (1777299)CaDiCaL version: 2.1.3
% 4.27/1.73 % (1777299)Termination reason: Instruction limit
% 4.27/1.73 % (1777299)Termination phase: Preprocessing 3
% 4.27/1.73 % (1777299)Time elapsed: 0.083 s
% 4.27/1.73 % (1777299)Peak memory usage: 93 MB
% 4.27/1.73 % (1777299)Instructions burned: 129 (million)
% 4.27/1.73 % (1777307)lrs+10_1_sil=8000:sp=occurrence:random_seed=1280720000:i=285:sd=3:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/285Mi)
% 4.27/1.73 % (1777308)lrs+10_1_sil=32000:urr=on:br=off:random_seed=838080301:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 4.27/1.73 % (1777309)lrs+1011_1_sil=32000:sp=occurrence:random_seed=653175289:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 4.27/1.73 % (1777309)Also succeeded, but the first one will report.
% 4.27/1.73 % (1777308)Instruction limit reached!
% 4.27/1.73 % (1777308)------------------------------
% 4.27/1.73 % (1777308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.73 % (1777308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.73 % (1777308)CaDiCaL version: 2.1.3
% 4.27/1.73 % (1777308)Termination reason: Instruction limit
% 4.27/1.73 % (1777308)Termination phase: Property scanning
% 4.27/1.73 % (1777308)Time elapsed: 0.070 s
% 4.27/1.73 % (1777308)Peak memory usage: 92 MB
% 4.27/1.73 % (1777308)Instructions burned: 158 (million)
% 4.27/1.73 % (1777307)Also succeeded, but the first one will report.
% 4.27/1.73 % (1777296)Refutation found. Thanks to Tanya!
% 4.27/1.73 % SZS status Theorem for theBenchmark
% 4.27/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 4.27/1.73 % (1777296)------------------------------
% 4.27/1.73 % (1777296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.73 % (1777296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.73 % (1777296)CaDiCaL version: 2.1.3
% 4.27/1.73 % (1777296)Termination reason: Refutation
% 4.27/1.73 % (1777296)Time elapsed: 0.039 s
% 4.27/1.73 % (1777296)Peak memory usage: 96 MB
% 4.27/1.73 % (1777296)Instructions burned: 57 (million)
% 4.27/1.73 % (1777296)------------------------------
% 4.27/1.73 % (1777296)------------------------------
% 4.27/1.73 % (1777288)Success in time 0.852 s
% 4.27/1.73 % Vampire exiting
%------------------------------------------------------------------------------