%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW367+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 : n006.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 01:30:12 PM UTC 2026
% Result : Theorem 4.38s 1.76s
% Output : Refutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 57 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 21 |; 12 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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; 0-4 aty)
% Number of variables : 53 ( 50 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),X0)))
<=> ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
& X3 = hAPP(X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
fof(f53,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/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(f5225,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5228,axiom,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f5230,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)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(f5231,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)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(negated_conjecture,[status(cth)],[f5230]) ).
fof(f5232,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)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(flattening,[],[f5231]) ).
fof(f5493,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),X0)))
| ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
| hAPP(X1,X5) != X3 ) )
& ( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
& X3 = hAPP(X1,X5) )
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),X0))) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f5494,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),X0)))
| ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
| hAPP(X1,X5) != X3 ) )
& ( ? [X6] :
( hBOOL(hAPP(hAPP(c_member(X2),X6),X0))
& hAPP(X1,X6) = X3 )
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),X0))) ) ),
inference(rectify,[],[f5493]) ).
fof(f5495,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),X0)))
| ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
| hAPP(X1,X5) != X3 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(X2),sK6(X0,X1,X2,X3)),X0))
& hAPP(X1,sK6(X0,X1,X2,X3)) = X3 )
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X6,sK6(X0,X1,X2,X3))],[f5494]) ).
fof(f5594,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,[],[f53]) ).
fof(f5595,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,[],[f5594]) ).
fof(f5604,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(cnf_transformation,[],[f5225]) ).
fof(f5607,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(cnf_transformation,[],[f5228]) ).
fof(f5609,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)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(cnf_transformation,[],[f5232]) ).
fof(f5660,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
| hAPP(X1,X5) != X3 ),
inference(cnf_transformation,[],[f5495]) ).
fof(f6022,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,[],[f5595]) ).
fof(f6127,plain,
! [X2,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X1,X5)),hAPP(c_Set_Oimage(X2,X4,X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X0)) ),
inference(equality_resolution,[],[f5660]) ).
fof(f6186,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)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(resolution,[],[f5609,f6022]) ).
fof(f6189,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,[],[f6186,f5604]) ).
fof(f6195,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(resolution,[],[f6189,f6127]) ).
fof(f6197,plain,
$false,
inference(forward_subsumption_resolution,[],[f6195,f5607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW367+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 13:42:10 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.38/1.76 % (3972961)Detected formulas, will run a generic FOF schedule.
% 4.38/1.76 % (3972970)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=781643575:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 4.38/1.76 % (3972971)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=491175197:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 4.38/1.76 % (3972970)Instruction limit reached!
% 4.38/1.76 % (3972970)------------------------------
% 4.38/1.76 % (3972970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3972970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3972970)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3972970)Termination reason: Instruction limit
% 4.38/1.76 % (3972970)Termination phase: Property scanning
% 4.38/1.76 % (3972970)Time elapsed: 0.040 s
% 4.38/1.76 % (3972970)Peak memory usage: 93 MB
% 4.38/1.76 % (3972970)Instructions burned: 125 (million)
% 4.38/1.76 % (3972966)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=744262850:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 4.38/1.76 % (3972967)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=2210774890:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 4.38/1.76 % (3972968)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=2206786370:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 4.38/1.76 % (3972969)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1550728085:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 4.38/1.76 % (3972972)dis-21_1_sil=8000:lcm=predicate:random_seed=2397561427: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 % (3972971)Instruction limit reached!
% 4.38/1.76 % (3972971)------------------------------
% 4.38/1.76 % (3972971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3972971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3972971)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3972971)Termination reason: Instruction limit
% 4.38/1.76 % (3972971)Termination phase: SInE selection
% 4.38/1.76 % (3972971)Time elapsed: 0.057 s
% 4.38/1.76 % (3972971)Peak memory usage: 90 MB
% 4.38/1.76 % (3972971)Instructions burned: 140 (million)
% 4.38/1.76 % (3972969)First to succeed.
% 4.38/1.76 % (3972969)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3972961"
% 4.38/1.76 % (3972979)lrs+10_1_sil=8000:sp=occurrence:random_seed=1897341483:i=285:sd=3:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/285Mi)
% 4.38/1.76 % (3972972)Instruction limit reached!
% 4.38/1.76 % (3972972)------------------------------
% 4.38/1.76 % (3972972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3972972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3972972)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3972972)Termination reason: Instruction limit
% 4.38/1.76 % (3972972)Termination phase: Preprocessing 3
% 4.38/1.76 % (3972972)Time elapsed: 0.086 s
% 4.38/1.76 % (3972972)Peak memory usage: 93 MB
% 4.38/1.76 % (3972972)Instructions burned: 129 (million)
% 4.38/1.76 % (3972979)Instruction limit reached!
% 4.38/1.76 % (3972979)------------------------------
% 4.38/1.76 % (3972979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3972979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3972979)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3972979)Termination reason: Instruction limit
% 4.38/1.76 % (3972979)Termination phase: Saturation
% 4.38/1.76 % (3972979)Time elapsed: 0.088 s
% 4.38/1.76 % (3972979)Peak memory usage: 96 MB
% 4.38/1.76 % (3972979)Instructions burned: 285 (million)
% 4.38/1.76 % (3972981)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1950872072:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/157Mi)
% 4.38/1.76 % (3972983)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1081678184:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 4.38/1.76 % (3972984)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=1652996354:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 4.38/1.76 % (3972981)Instruction limit reached!
% 4.38/1.76 % (3972981)------------------------------
% 4.38/1.76 % (3972981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.76 % (3972981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.76 % (3972981)CaDiCaL version: 2.1.3
% 4.38/1.76 % (3972981)Termination reason: Instruction limit
% 4.38/1.76 % (3972981)Termination phase: Property scanning
% 4.38/1.76 % (3972981)Time elapsed: 0.074 s
% 4.38/1.76 % (3972981)Peak memory usage: 91 MB
% 4.38/1.76 % (3972981)Instructions burned: 159 (million)
% 4.38/1.76 % (3972969)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 % (3972969)------------------------------
% 4.38/1.76 % (3972969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.77 % (3972969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.77 % (3972969)CaDiCaL version: 2.1.3
% 4.38/1.77 % (3972969)Termination reason: Refutation
% 4.38/1.77 % (3972969)Time elapsed: 0.064 s
% 4.38/1.77 % (3972969)Peak memory usage: 95 MB
% 4.38/1.77 % (3972969)Instructions burned: 109 (million)
% 4.38/1.77 % (3972969)------------------------------
% 4.38/1.77 % (3972969)------------------------------
% 4.38/1.77 % (3972961)Success in time 0.874 s
% 4.38/1.77 % Vampire exiting
%------------------------------------------------------------------------------