%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW470+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 01:30:25 PM UTC 2026
% Result : Theorem 6.43s 1.82s
% Output : Refutation 6.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 15 unt; 0 def)
% Number of atoms : 32 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 5 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 40 ( 40 usr; 19 con; 0-4 aty)
% Number of variables : 31 ( 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
is_bool(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).
fof(f41,axiom,
! [X0,X1,X2,X3] :
( ! [X4,X5] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X4),X5))
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(X0),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),X5)),X1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(X2,X4)))),bot_bo797238721a_bool))) )
=> hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(X0),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(X3,X1,X2)),bot_bo797238721a_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).
fof(f1242,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f1264,axiom,
! [X0,X1] :
( is_bool(X0)
=> hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X0),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
fof(f1287,axiom,
! [X0,X1] : hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).
fof(f1399,conjecture,
hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo797238721a_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1400,negated_conjecture,
~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo797238721a_bool))),
inference(negated_conjecture,[status(cth)],[f1399]) ).
fof(f1401,plain,
~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo797238721a_bool))),
inference(flattening,[],[f1400]) ).
fof(f1415,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(X0),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(X3,X1,X2)),bot_bo797238721a_bool)))
| ? [X4,X5] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(X0),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),X5)),X1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(X2,X4)))),bot_bo797238721a_bool)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,X4),X5)) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f1416,plain,
! [X0,X1] :
( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X0),X1) = X0
| ~ is_bool(X0) ),
inference(ennf_transformation,[],[f1264]) ).
fof(f1433,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(X0),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(X3,X1,X2)),bot_bo797238721a_bool)))
| ( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(X0),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),sK9(X0,X1,X2,X3))),X1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_a2036067514e_bool(X2,sK8(X0,X1,X2,X3))))),bot_bo797238721a_bool)))
& hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK8(X0,X1,X2,X3)),sK9(X0,X1,X2,X3))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1,X2,X3)),skolemize(X5,sK9(X0,X1,X2,X3))],[f1415]) ).
fof(f1434,plain,
~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo797238721a_bool))),
inference(cnf_transformation,[],[f1401]) ).
fof(f1435,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f1242]) ).
fof(f1436,plain,
is_bool(fFalse),
inference(cnf_transformation,[],[f23]) ).
fof(f1476,plain,
! [X0,X1] : hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X0),X1) = X0,
inference(cnf_transformation,[],[f1287]) ).
fof(f1477,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X3,sK8(X0,X1,X2,X3)),sK9(X0,X1,X2,X3)))
| hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(X0),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(X3,X1,X2)),bot_bo797238721a_bool))) ),
inference(cnf_transformation,[],[f1433]) ).
fof(f1482,plain,
! [X0,X1] :
( ~ is_bool(X0)
| hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X0),X1) = X0 ),
inference(cnf_transformation,[],[f1416]) ).
fof(f1514,plain,
! [X0] : fFalse = hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse),X0),
inference(unit_resulting_resolution,[],[f1482,f1436]) ).
fof(f1663,plain,
hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),sK8(g,c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)))),sK9(g,c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse))))),
inference(unit_resulting_resolution,[],[f1477,f1434]) ).
fof(f1668,plain,
hBOOL(hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse),sK9(g,c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse))))),
inference(forward_demodulation,[],[f1663,f1476]) ).
fof(f1670,plain,
hBOOL(fFalse),
inference(forward_demodulation,[],[f1668,f1514]) ).
fof(f1672,plain,
$false,
inference(forward_subsumption_resolution,[],[f1670,f1435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:02:37 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 4.71/1.57 % (367671)Detected formulas, will run a generic FOF schedule.
% 4.71/1.57 % (367812)dis-21_1_sil=8000:lcm=predicate:random_seed=1172838750: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)
% 4.71/1.57 % (367808)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=3817818255:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.71/1.57 % (367806)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=1807046463:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.71/1.57 % (367809)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3318414286:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.71/1.57 % (367807)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=1206682854:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.71/1.57 % (367809)Refutation not found, incomplete strategy
% 4.71/1.57 % (367809)------------------------------
% 4.71/1.57 % (367809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.57 % (367809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.57 % (367809)CaDiCaL version: 2.1.3
% 4.71/1.57 % (367809)Termination reason: Refutation not found, incomplete strategy
% 4.71/1.57 % (367809)Time elapsed: 0.015 s
% 4.71/1.57 % (367809)Peak memory usage: 89 MB
% 4.71/1.57 % (367809)Instructions burned: 12 (million)
% 4.71/1.57 % (367810)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=961266633:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.71/1.57 % (367812)Instruction limit reached!
% 4.71/1.57 % (367812)------------------------------
% 4.71/1.57 % (367812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.57 % (367812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.57 % (367812)CaDiCaL version: 2.1.3
% 4.71/1.57 % (367812)Termination reason: Instruction limit
% 4.71/1.57 % (367812)Termination phase: Property scanning
% 4.71/1.57 % (367812)Time elapsed: 0.058 s
% 4.71/1.57 % (367812)Peak memory usage: 89 MB
% 4.71/1.57 % (367812)Instructions burned: 130 (million)
% 4.71/1.57 % (367811)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4060447646:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.71/1.57 % (367811)Instruction limit reached!
% 4.71/1.57 % (367811)------------------------------
% 4.71/1.57 % (367811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.57 % (367811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.57 % (367811)CaDiCaL version: 2.1.3
% 4.71/1.57 % (367811)Termination reason: Instruction limit
% 4.71/1.57 % (367811)Termination phase: Saturation
% 4.71/1.57 % (367811)Time elapsed: 0.063 s
% 4.71/1.57 % (367811)Peak memory usage: 90 MB
% 4.71/1.57 % (367811)Instructions burned: 141 (million)
% 4.71/1.57 % (367810)Instruction limit reached!
% 4.71/1.57 % (367810)------------------------------
% 4.71/1.57 % (367810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.57 % (367810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.57 % (367810)CaDiCaL version: 2.1.3
% 4.71/1.57 % (367810)Termination reason: Instruction limit
% 4.71/1.57 % (367810)Termination phase: Saturation
% 4.71/1.57 % (367810)Time elapsed: 0.119 s
% 4.71/1.57 % (367810)Peak memory usage: 89 MB
% 4.71/1.57 % (367810)Instructions burned: 120 (million)
% 4.71/1.57 % (367838)lrs+10_1_sil=8000:sp=occurrence:random_seed=2383178756:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 4.71/1.57 % (367843)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1965523941:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.71/1.57 % (367809)------------------------------
% 4.71/1.57 % (367809)------------------------------
% 4.71/1.57 % (367843)First to succeed.
% 4.71/1.57 % (367843)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-367671"
% 4.71/1.57 % (367845)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3029850793:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 4.71/1.57 % (367851)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=3282360074:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 6.43/1.82 % (367843)Refutation found. Thanks to Tanya!
% 6.43/1.82 % SZS status Theorem for theBenchmark
% 6.43/1.82 % SZS output start Proof for theBenchmark
% See solution above
% 6.43/1.82 % (367843)------------------------------
% 6.43/1.82 % (367843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.43/1.82 % (367843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.43/1.82 % (367843)CaDiCaL version: 2.1.3
% 6.43/1.82 % (367843)Termination reason: Refutation
% 6.43/1.82 % (367843)Time elapsed: 0.031 s
% 6.43/1.82 % (367843)Peak memory usage: 90 MB
% 6.43/1.82 % (367843)Instructions burned: 59 (million)
% 6.43/1.82 % (367843)------------------------------
% 6.43/1.82 % (367843)------------------------------
% 6.43/1.82 % (367671)Success in time 0.884 s
% 6.43/1.82 % Vampire exiting
%------------------------------------------------------------------------------