%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW394+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 : n018.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 01:30:15 PM UTC 2026
% Result : Theorem 4.22s 1.88s
% Output : Refutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 30 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 28 ( 12 ~; 10 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f135,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0))
=> c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_asm) ).
fof(f247,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(f5224,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),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(f5225,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5224]) ).
fof(f5226,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(flattening,[],[f5225]) ).
fof(f5244,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0)) ),
inference(ennf_transformation,[],[f135]) ).
fof(f5515,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
& X0 != X1 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X1 = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ) ),
inference(nnf_transformation,[],[f247]) ).
fof(f5516,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
& X0 != X1 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X1 = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ) ),
inference(flattening,[],[f5515]) ).
fof(f5589,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5226]) ).
fof(f5593,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1) ),
inference(cnf_transformation,[],[f5244]) ).
fof(f5782,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f5516]) ).
fof(f6067,plain,
! [X2,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X1)),
inference(equality_resolution,[],[f5782]) ).
fof(f6268,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X1),
inference(resolution,[],[f5593,f6067]) ).
fof(f6270,plain,
$false,
inference(resolution,[],[f6268,f5589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW394+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n018.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 13:48:40 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 Running first-order theorem proving
% 0.11/0.26 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
% 4.22/1.88 % (3392478)Detected formulas, will run a generic FOF schedule.
% 4.22/1.88 % (3392598)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=992875908:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 4.22/1.88 % (3392594)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=4035272853:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 4.22/1.88 % (3392596)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=2413903589:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 4.22/1.88 % (3392597)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=4124658718:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 4.22/1.88 % (3392602)dis-21_1_sil=8000:lcm=predicate:random_seed=3345402103: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)
% 4.22/1.88 % (3392598)Instruction limit reached!
% 4.22/1.88 % (3392598)------------------------------
% 4.22/1.88 % (3392598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.88 % (3392598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.88 % (3392598)CaDiCaL version: 2.1.3
% 4.22/1.88 % (3392598)Termination reason: Instruction limit
% 4.22/1.88 % (3392598)Termination phase: Saturation
% 4.22/1.88 % (3392598)Time elapsed: 0.041 s
% 4.22/1.88 % (3392598)Peak memory usage: 94 MB
% 4.22/1.88 % (3392598)Instructions burned: 111 (million)
% 4.22/1.88 % (3392599)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=642080000:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 4.22/1.88 % (3392600)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3096945693:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 4.22/1.88 % (3392600)Instruction limit reached!
% 4.22/1.88 % (3392600)------------------------------
% 4.22/1.88 % (3392600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.88 % (3392600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.88 % (3392600)CaDiCaL version: 2.1.3
% 4.22/1.88 % (3392600)Termination reason: Instruction limit
% 4.22/1.88 % (3392600)Termination phase: SInE selection
% 4.22/1.88 % (3392600)Time elapsed: 0.059 s
% 4.22/1.88 % (3392600)Peak memory usage: 90 MB
% 4.22/1.88 % (3392600)Instructions burned: 140 (million)
% 4.22/1.88 % (3392599)Instruction limit reached!
% 4.22/1.88 % (3392599)------------------------------
% 4.22/1.88 % (3392599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.88 % (3392599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.88 % (3392599)CaDiCaL version: 2.1.3
% 4.22/1.88 % (3392599)Termination reason: Instruction limit
% 4.22/1.88 % (3392599)Termination phase: Saturation
% 4.22/1.88 % (3392599)Time elapsed: 0.067 s
% 4.22/1.88 % (3392599)Peak memory usage: 94 MB
% 4.22/1.88 % (3392599)Instructions burned: 119 (million)
% 4.22/1.88 % (3392602)Instruction limit reached!
% 4.22/1.88 % (3392602)------------------------------
% 4.22/1.88 % (3392602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.88 % (3392602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.88 % (3392602)CaDiCaL version: 2.1.3
% 4.22/1.88 % (3392602)Termination reason: Instruction limit
% 4.22/1.88 % (3392602)Termination phase: Preprocessing 3
% 4.22/1.88 % (3392602)Time elapsed: 0.086 s
% 4.22/1.88 % (3392602)Peak memory usage: 93 MB
% 4.22/1.88 % (3392602)Instructions burned: 129 (million)
% 4.22/1.88 % (3392620)lrs+10_1_sil=8000:sp=occurrence:random_seed=1711770041:i=285:sd=3:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/285Mi)
% 4.22/1.88 % (3392620)First to succeed.
% 4.22/1.88 % (3392620)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3392478"
% 4.22/1.88 % (3392651)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3981391829:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 4.22/1.88 % (3392658)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4082674858:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 4.22/1.88 % (3392664)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=78548555:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 4.22/1.88 % (3392651)Instruction limit reached!
% 4.22/1.88 % (3392651)------------------------------
% 4.22/1.88 % (3392651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.88 % (3392651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.88 % (3392651)CaDiCaL version: 2.1.3
% 4.22/1.88 % (3392651)Termination reason: Instruction limit
% 4.22/1.88 % (3392651)Termination phase: Property scanning
% 4.22/1.88 % (3392651)Time elapsed: 0.070 s
% 4.22/1.88 % (3392651)Peak memory usage: 91 MB
% 4.22/1.88 % (3392651)Instructions burned: 157 (million)
% 4.22/1.88 % (3392620)Refutation found. Thanks to Tanya!
% 4.22/1.88 % SZS status Theorem for theBenchmark
% 4.22/1.88 % SZS output start Proof for theBenchmark
% See solution above
% 4.22/1.88 % (3392620)------------------------------
% 4.22/1.88 % (3392620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.22/1.88 % (3392620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.22/1.88 % (3392620)CaDiCaL version: 2.1.3
% 4.22/1.88 % (3392620)Termination reason: Refutation
% 4.22/1.88 % (3392620)Time elapsed: 0.030 s
% 4.22/1.88 % (3392620)Peak memory usage: 94 MB
% 4.22/1.88 % (3392620)Instructions burned: 83 (million)
% 4.22/1.88 % (3392620)------------------------------
% 4.22/1.88 % (3392620)------------------------------
% 4.22/1.88 % (3392478)Success in time 0.835 s
% 4.22/1.88 % Vampire exiting
%------------------------------------------------------------------------------