%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW473+6 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 01:30:30 PM UTC 2026
% Result : Theorem 5.85s 1.83s
% Output : Refutation 5.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 11 |; 5 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f133,axiom,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_imageI) ).
fof(f139,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
<=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_insert__subset) ).
fof(f604,axiom,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f607,axiom,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f609,conjecture,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(f610,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(negated_conjecture,[status(cth)],[f609]) ).
fof(f611,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(flattening,[],[f610]) ).
fof(f684,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(ennf_transformation,[],[f133]) ).
fof(f873,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3)) ) ),
inference(nnf_transformation,[],[f139]) ).
fof(f874,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3)) ) ),
inference(flattening,[],[f873]) ).
fof(f890,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cnf_transformation,[],[f604]) ).
fof(f893,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(cnf_transformation,[],[f607]) ).
fof(f895,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cnf_transformation,[],[f611]) ).
fof(f1045,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(cnf_transformation,[],[f684]) ).
fof(f1168,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f874]) ).
fof(f1236,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(resolution,[],[f895,f1168]) ).
fof(f1238,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(forward_subsumption_resolution,[],[f1236,f890]) ).
fof(f1248,plain,
~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(resolution,[],[f1238,f1045]) ).
fof(f1250,plain,
$false,
inference(forward_subsumption_resolution,[],[f1248,f893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n013.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Mon Sep 28 14:05:52 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running first-order theorem proving
% 0.24/0.30 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
% 4.85/1.66 % (1196996)Detected formulas, will run a generic FOF schedule.
% 4.85/1.66 % (1197016)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2905200703:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.85/1.66 % (1197017)dis-21_1_sil=8000:lcm=predicate:random_seed=3027577642: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)
% 4.85/1.66 % (1197017)Instruction limit reached!
% 4.85/1.66 % (1197017)------------------------------
% 4.85/1.66 % (1197017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (1197017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (1197017)CaDiCaL version: 2.1.3
% 4.85/1.66 % (1197017)Termination reason: Instruction limit
% 4.85/1.66 % (1197017)Termination phase: Property scanning
% 4.85/1.66 % (1197017)Time elapsed: 0.055 s
% 4.85/1.66 % (1197017)Peak memory usage: 87 MB
% 4.85/1.66 % (1197017)Instructions burned: 130 (million)
% 4.85/1.66 % (1197016)Instruction limit reached!
% 4.85/1.66 % (1197016)------------------------------
% 4.85/1.66 % (1197016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (1197016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (1197016)CaDiCaL version: 2.1.3
% 4.85/1.66 % (1197016)Termination reason: Instruction limit
% 4.85/1.66 % (1197016)Termination phase: Saturation
% 4.85/1.66 % (1197016)Time elapsed: 0.058 s
% 4.85/1.66 % (1197016)Peak memory usage: 89 MB
% 4.85/1.66 % (1197016)Instructions burned: 139 (million)
% 4.85/1.66 % (1197014)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1640546223:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.85/1.66 % (1197013)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=923524768:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.85/1.66 % (1197011)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=2884688473:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.85/1.66 % (1197012)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=1530823806:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.85/1.66 % (1197015)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2832887581:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.85/1.66 % (1197014)First to succeed.
% 4.85/1.66 % (1197014)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1196996"
% 4.85/1.66 % (1197024)lrs+10_1_sil=8000:sp=occurrence:random_seed=4144361779:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.85/1.66 % (1197015)Instruction limit reached!
% 4.85/1.66 % (1197015)------------------------------
% 4.85/1.66 % (1197015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (1197015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (1197015)CaDiCaL version: 2.1.3
% 4.85/1.66 % (1197015)Termination reason: Instruction limit
% 4.85/1.66 % (1197015)Termination phase: Saturation
% 4.85/1.66 % (1197015)Time elapsed: 0.109 s
% 4.85/1.66 % (1197015)Peak memory usage: 89 MB
% 4.85/1.66 % (1197015)Instructions burned: 119 (million)
% 4.85/1.66 % (1197025)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1738946074:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.85/1.66 % (1197024)Instruction limit reached!
% 4.85/1.66 % (1197024)------------------------------
% 4.85/1.66 % (1197024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (1197024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (1197024)CaDiCaL version: 2.1.3
% 4.85/1.66 % (1197024)Termination reason: Instruction limit
% 4.85/1.66 % (1197024)Termination phase: Saturation
% 4.85/1.66 % (1197024)Time elapsed: 0.143 s
% 4.85/1.66 % (1197024)Peak memory usage: 91 MB
% 4.85/1.66 % (1197024)Instructions burned: 286 (million)
% 4.85/1.66 % (1197025)Instruction limit reached!
% 4.85/1.66 % (1197025)------------------------------
% 4.85/1.66 % (1197025)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (1197025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.83 % (1197025)CaDiCaL version: 2.1.3
% 5.85/1.83 % (1197025)Termination reason: Instruction limit
% 5.85/1.83 % (1197025)Termination phase: Saturation
% 5.85/1.83 % (1197025)Time elapsed: 0.148 s
% 5.85/1.83 % (1197025)Peak memory usage: 90 MB
% 5.85/1.83 % (1197025)Instructions burned: 158 (million)
% 5.85/1.83 % (1197028)lrs+1011_1_sil=32000:sp=occurrence:random_seed=870065324:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 5.85/1.83 % (1197030)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=912893334:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 5.85/1.83 % (1197014)Refutation found. Thanks to Tanya!
% 5.85/1.83 % SZS status Theorem for theBenchmark
% 5.85/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 5.85/1.83 % (1197014)------------------------------
% 5.85/1.83 % (1197014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.83 % (1197014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.83 % (1197014)CaDiCaL version: 2.1.3
% 5.85/1.83 % (1197014)Termination reason: Refutation
% 5.85/1.83 % (1197014)Time elapsed: 0.076 s
% 5.85/1.83 % (1197014)Peak memory usage: 89 MB
% 5.85/1.83 % (1197014)Instructions burned: 92 (million)
% 5.85/1.83 % (1197014)------------------------------
% 5.85/1.83 % (1197014)------------------------------
% 5.85/1.83 % (1196996)Success in time 0.763 s
% 5.85/1.83 % Vampire exiting
%------------------------------------------------------------------------------