%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV834-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 01:19:37 PM UTC 2026
% Result : Unsatisfiable 3.77s 1.23s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 11 ( 10 unt; 0 def)
% Number of atoms : 12 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 3 ( 2 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-4 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,axiom,
! [X0,X1] : c_Collect(X0,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f669,axiom,
! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(f688,axiom,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__def_0) ).
fof(f707,axiom,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f719,axiom,
! [X2,X3,X0,X1] : hAPP(c_COMBK(X0,X1,X2),X3) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f725,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f762,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_COMBK(c_False,tc_bool,X0),
inference(superposition,[],[f44,f688]) ).
fof(f1068,plain,
hBOOL(hAPP(hAPP(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))),
inference(resolution,[],[f669,f725]) ).
fof(f1072,plain,
hBOOL(hAPP(hAPP(c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))),
inference(forward_demodulation,[],[f1068,f762]) ).
fof(f1073,plain,
hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),v_c))),
inference(forward_demodulation,[],[f1072,f719]) ).
fof(f1074,plain,
$false,
inference(forward_subsumption_resolution,[],[f1073,f707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV834-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 12:41:21 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.77/1.23 % (326965)Input is clausal, will run a generic CNF schedule.
% 3.77/1.23 % (326972)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=762034676:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.77/1.23 % (326973)lrs+10_1_sil=8000:sp=occurrence:random_seed=3153428021:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.77/1.23 % (326970)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=137034111:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.77/1.23 % (326971)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=823781087:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.77/1.23 % (326975)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1898471469:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.77/1.23 % (326974)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=599952982:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.77/1.23 % (326976)dis-21_1_sil=8000:lcm=predicate:random_seed=3182709315:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.77/1.23 % (326975)First to succeed.
% 3.77/1.23 % (326975)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-326965"
% 3.77/1.23 % (326976)Instruction limit reached!
% 3.77/1.23 % (326976)------------------------------
% 3.77/1.23 % (326976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.23 % (326976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.23 % (326976)CaDiCaL version: 2.1.3
% 3.77/1.23 % (326976)Termination reason: Instruction limit
% 3.77/1.23 % (326976)Termination phase: Saturation
% 3.77/1.23 % (326976)Time elapsed: 0.048 s
% 3.77/1.23 % (326976)Peak memory usage: 88 MB
% 3.77/1.23 % (326976)Instructions burned: 119 (million)
% 3.77/1.23 % (326973)Instruction limit reached!
% 3.77/1.23 % (326973)------------------------------
% 3.77/1.23 % (326973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.23 % (326973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.23 % (326973)CaDiCaL version: 2.1.3
% 3.77/1.23 % (326973)Termination reason: Instruction limit
% 3.77/1.23 % (326973)Termination phase: Saturation
% 3.77/1.23 % (326973)Time elapsed: 0.061 s
% 3.77/1.23 % (326973)Peak memory usage: 89 MB
% 3.77/1.23 % (326973)Instructions burned: 107 (million)
% 3.77/1.23 % (326974)Instruction limit reached!
% 3.77/1.23 % (326974)------------------------------
% 3.77/1.23 % (326974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.23 % (326974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.23 % (326974)CaDiCaL version: 2.1.3
% 3.77/1.23 % (326974)Termination reason: Instruction limit
% 3.77/1.23 % (326974)Termination phase: Saturation
% 3.77/1.23 % (326974)Time elapsed: 0.068 s
% 3.77/1.23 % (326974)Peak memory usage: 88 MB
% 3.77/1.23 % (326974)Instructions burned: 114 (million)
% 3.77/1.23 % (326985)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1670230908:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.77/1.23 % (326985)Refutation not found, incomplete strategy
% 3.77/1.23 % (326985)------------------------------
% 3.77/1.23 % (326985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.23 % (326985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.23 % (326985)CaDiCaL version: 2.1.3
% 3.77/1.23 % (326985)Termination reason: Refutation not found, incomplete strategy
% 3.77/1.23 % (326985)Time elapsed: 0.017 s
% 3.77/1.23 % (326985)Peak memory usage: 88 MB
% 3.77/1.23 % (326985)Instructions burned: 27 (million)
% 3.77/1.23 % (326986)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=994653535:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.77/1.23 % (326987)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1546074464:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.77/1.23 % (326986)Instruction limit reached!
% 3.77/1.23 % (326986)------------------------------
% 3.77/1.23 % (326986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.23 % (326986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.23 % (326986)CaDiCaL version: 2.1.3
% 3.77/1.23 % (326986)Termination reason: Instruction limit
% 3.77/1.23 % (326986)Termination phase: Saturation
% 3.77/1.23 % (326986)Time elapsed: 0.099 s
% 3.77/1.23 % (326986)Peak memory usage: 90 MB
% 3.77/1.23 % (326986)Instructions burned: 190 (million)
% 3.77/1.23 % (326975)Refutation found. Thanks to Tanya!
% 3.77/1.23 % SZS status Unsatisfiable for theBenchmark
% 3.77/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.23 % (326975)------------------------------
% 3.77/1.23 % (326975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.23 % (326975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.23 % (326975)CaDiCaL version: 2.1.3
% 3.77/1.23 % (326975)Termination reason: Refutation
% 3.77/1.23 % (326975)Time elapsed: 0.045 s
% 3.77/1.23 % (326975)Peak memory usage: 89 MB
% 3.77/1.23 % (326975)Instructions burned: 75 (million)
% 3.77/1.23 % (326975)------------------------------
% 3.77/1.23 % (326975)------------------------------
% 3.77/1.23 % (326965)Success in time 0.488 s
% 3.77/1.23 % Vampire exiting
%------------------------------------------------------------------------------