%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW362+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:30:11 PM UTC 2026
% Result : Theorem 4.38s 1.76s
% Output : Refutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 50 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 49 ( 24 ~; 17 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(f7,axiom,
! [X0,X1,X2,X3,X4,X5] :
( X5 = hAPP(X4,X3)
=> ( hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
=> hBOOL(hAPP(hAPP(c_member(X0),X5),hAPP(c_Set_Oimage(X2,X0,X4),X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(f67,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3),X2),X1)),X0))
<=> ( hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(f5225,axiom,
v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f5226,axiom,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f5227,conjecture,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(f5228,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(negated_conjecture,[status(cth)],[f5227]) ).
fof(f5229,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(flattening,[],[f5228]) ).
fof(f5247,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),X5),hAPP(c_Set_Oimage(X2,X0,X4),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hAPP(X4,X3) != X5 ),
inference(ennf_transformation,[],[f7]) ).
fof(f5248,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),X5),hAPP(c_Set_Oimage(X2,X0,X4),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hAPP(X4,X3) != X5 ),
inference(flattening,[],[f5247]) ).
fof(f5362,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3),X2),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X0)) )
& ( ( hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3),X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f5363,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3),X2),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X0)) )
& ( ( hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3),X2),X1)),X0)) ) ),
inference(flattening,[],[f5362]) ).
fof(f5375,plain,
v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(cnf_transformation,[],[f5225]) ).
fof(f5376,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(cnf_transformation,[],[f5226]) ).
fof(f5377,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(cnf_transformation,[],[f5229]) ).
fof(f5415,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),X5),hAPP(c_Set_Oimage(X2,X0,X4),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hAPP(X4,X3) != X5 ),
inference(cnf_transformation,[],[f5248]) ).
fof(f5472,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f5516,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3),X2),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X0)) ),
inference(cnf_transformation,[],[f5363]) ).
fof(f5561,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X0),hAPP(X4,X3)),hAPP(c_Set_Oimage(X2,X0,X4),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(equality_resolution,[],[f5415]) ).
fof(f5609,plain,
( ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(resolution,[],[f5377,f5516]) ).
fof(f5613,plain,
~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(forward_subsumption_resolution,[],[f5609,f5472]) ).
fof(f5615,plain,
~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
inference(forward_demodulation,[],[f5613,f5375]) ).
fof(f5658,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,X0)),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_U)) ),
inference(superposition,[],[f5561,f5375]) ).
fof(f6200,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(resolution,[],[f5658,f5615]) ).
fof(f6210,plain,
$false,
inference(forward_subsumption_resolution,[],[f6200,f5376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW362+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n017.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 13:37:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 4.38/1.76 % (3554137)Detected formulas, will run a generic FOF schedule.
% 4.38/1.76 % (3554147)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1006062581:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 4.38/1.76 % (3554145)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1322138070:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 4.38/1.76 % (3554142)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=1537375011:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 4.38/1.76 % (3554143)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=304821568:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 4.38/1.76 % (3554144)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=2711841467:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 4.38/1.76 % (3554148)dis-21_1_sil=8000:lcm=predicate:random_seed=2195032109: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)
% 4.38/1.76 % (3554146)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3916044102:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 4.38/1.76 % (3554147)Instruction limit reached!
% 4.38/1.76 % (3554147)------------------------------
% 4.38/1.76 % (3554147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3554147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3554147)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3554147)Termination reason: Instruction limit
% 4.38/1.76 % (3554147)Termination phase: SInE selection
% 4.38/1.76 % (3554147)Time elapsed: 0.033 s
% 4.38/1.76 % (3554147)Peak memory usage: 90 MB
% 4.38/1.76 % (3554147)Instructions burned: 141 (million)
% 4.38/1.76 % (3554145)First to succeed.
% 4.38/1.76 % (3554145)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3554137"
% 4.38/1.76 % (3554146)Instruction limit reached!
% 4.38/1.76 % (3554146)------------------------------
% 4.38/1.76 % (3554146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3554146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3554146)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3554146)Termination reason: Instruction limit
% 4.38/1.76 % (3554146)Termination phase: Saturation
% 4.38/1.76 % (3554146)Time elapsed: 0.072 s
% 4.38/1.76 % (3554146)Peak memory usage: 94 MB
% 4.38/1.76 % (3554146)Instructions burned: 119 (million)
% 4.38/1.76 % (3554156)lrs+10_1_sil=8000:sp=occurrence:random_seed=2197804538:i=285:sd=3:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/285Mi)
% 4.38/1.76 % (3554148)Instruction limit reached!
% 4.38/1.76 % (3554148)------------------------------
% 4.38/1.76 % (3554148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3554148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3554148)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3554148)Termination reason: Instruction limit
% 4.38/1.76 % (3554148)Termination phase: Preprocessing 3
% 4.38/1.76 % (3554148)Time elapsed: 0.107 s
% 4.38/1.76 % (3554148)Peak memory usage: 93 MB
% 4.38/1.76 % (3554148)Instructions burned: 130 (million)
% 4.38/1.76 % (3554157)lrs+10_1_sil=32000:urr=on:br=off:random_seed=292583412:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 4.38/1.76 % (3554156)Instruction limit reached!
% 4.38/1.76 % (3554156)------------------------------
% 4.38/1.76 % (3554156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3554156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3554156)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3554156)Termination reason: Instruction limit
% 4.38/1.76 % (3554156)Termination phase: Saturation
% 4.38/1.76 % (3554156)Time elapsed: 0.099 s
% 4.38/1.76 % (3554156)Peak memory usage: 96 MB
% 4.38/1.76 % (3554156)Instructions burned: 288 (million)
% 4.38/1.76 % (3554159)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2806232516:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 4.38/1.76 % (3554157)Instruction limit reached!
% 4.38/1.76 % (3554157)------------------------------
% 4.38/1.76 % (3554157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3554157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3554157)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3554157)Termination reason: Instruction limit
% 4.38/1.76 % (3554157)Termination phase: Property scanning
% 4.38/1.76 % (3554157)Time elapsed: 0.073 s
% 4.38/1.76 % (3554157)Peak memory usage: 92 MB
% 4.38/1.76 % (3554157)Instructions burned: 160 (million)
% 4.38/1.76 % (3554161)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=850693534:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 4.38/1.76 % (3554145)Refutation found. Thanks to Tanya!
% 4.38/1.76 % SZS status Theorem for theBenchmark
% 4.38/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 4.38/1.76 % (3554145)------------------------------
% 4.38/1.76 % (3554145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3554145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3554145)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3554145)Termination reason: Refutation
% 4.38/1.76 % (3554145)Time elapsed: 0.057 s
% 4.38/1.76 % (3554145)Peak memory usage: 95 MB
% 4.38/1.76 % (3554145)Instructions burned: 87 (million)
% 4.38/1.76 % (3554145)------------------------------
% 4.38/1.76 % (3554145)------------------------------
% 4.38/1.76 % (3554137)Success in time 0.867 s
% 4.38/1.76 % Vampire exiting
%------------------------------------------------------------------------------