%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 01:46:08 PM UTC 2026
% Result : Unsatisfiable 5.47s 1.60s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X2,X0,X1] : aux2(X0,X1,X2,bfalse) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(f5,plain,
! [X2,X0,X1] : bfalse = aux2(X0,X1,X2,bfalse),
inference(reorient_equations,[],[f4]) ).
fof(f8,axiom,
! [X0] : leqNat(s(X0),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f9,plain,
! [X0] : bfalse = leqNat(s(X0),z),
inference(reorient_equations,[],[f8]) ).
fof(f11,axiom,
! [X0] : merge(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f15,axiom,
ord(nil) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(f16,plain,
btrue = ord(nil),
inference(reorient_equations,[],[f15]) ).
fof(f19,axiom,
! [X2,X0,X1] : ord(cons(X0,cons(X1,X2))) = aux2(X0,X1,X2,leqNat(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(f20,axiom,
! [X0] : impl(btrue,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(f23,axiom,
! [X0,X1] : prop_merge_ord_not3(X0,X1) = impl(eq2(ord(X0),btrue),impl(eq2(ord(X1),bfalse),eq2(ord(merge(X0,X1)),btrue))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(f24,axiom,
eq2(bfalse,btrue) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
fof(f25,plain,
bfalse = eq2(bfalse,btrue),
inference(reorient_equations,[],[f24]) ).
fof(f35,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
fof(f36,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
! [X0,X1] : eq2(prop_merge_ord_not3(X0,X1),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f38,plain,
! [X0,X1] : btrue != eq2(prop_merge_ord_not3(X0,X1),bfalse),
inference(reorient_equations,[],[f37]) ).
fof(f52,plain,
! [X0,X1] : ord(cons(s(X0),cons(z,X1))) = aux2(s(X0),z,X1,bfalse),
inference(superposition,[],[f19,f9]) ).
fof(f54,plain,
! [X0,X1] : bfalse = ord(cons(s(X0),cons(z,X1))),
inference(forward_demodulation,[],[f52,f5]) ).
fof(f91,plain,
! [X0] : prop_merge_ord_not3(nil,X0) = impl(eq2(ord(nil),btrue),impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))),
inference(superposition,[],[f23,f11]) ).
fof(f100,plain,
! [X0] : prop_merge_ord_not3(nil,X0) = impl(eq2(btrue,btrue),impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))),
inference(forward_demodulation,[],[f91,f16]) ).
fof(f114,plain,
! [X0] : prop_merge_ord_not3(nil,X0) = impl(btrue,impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue))),
inference(forward_demodulation,[],[f100,f36]) ).
fof(f128,plain,
! [X0] : prop_merge_ord_not3(nil,X0) = impl(eq2(ord(X0),bfalse),eq2(ord(X0),btrue)),
inference(forward_demodulation,[],[f114,f20]) ).
fof(f161,plain,
! [X0,X1] : prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))) = impl(eq2(bfalse,bfalse),eq2(bfalse,btrue)),
inference(superposition,[],[f128,f54]) ).
fof(f168,plain,
! [X0,X1] : prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))) = impl(eq2(bfalse,bfalse),bfalse),
inference(forward_demodulation,[],[f161,f25]) ).
fof(f173,plain,
! [X0,X1] : prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))) = impl(btrue,bfalse),
inference(forward_demodulation,[],[f168,f36]) ).
fof(f178,plain,
! [X0,X1] : bfalse = prop_merge_ord_not3(nil,cons(s(X0),cons(z,X1))),
inference(forward_demodulation,[],[f173,f20]) ).
fof(f184,plain,
btrue != eq2(bfalse,bfalse),
inference(superposition,[],[f38,f178]) ).
fof(f185,plain,
$false,
inference(forward_subsumption_resolution,[],[f184,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n008.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Mon Sep 28 15:08:39 UTC 2026
% 0.25/0.28 % CPUTime :
% 0.25/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.33 Running first-order theorem proving
% 0.25/0.33 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
% 5.47/1.60 % (2321910)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.47/1.60 % (2321915)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=4063178277:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.47/1.60 % (2321921)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2985935328:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.47/1.60 % (2321917)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3096218283:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.47/1.60 % (2321918)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1099469573:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.47/1.60 % (2321919)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3017859886:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.47/1.60 % (2321920)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3525853384:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.47/1.60 % (2321916)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=257999446:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.47/1.60 % (2321919)Also succeeded, but the first one will report.
% 5.47/1.60 % (2321921)First to succeed.
% 5.47/1.60 % (2321921)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2321910"
% 5.47/1.60 % (2321918)Instruction limit reached!
% 5.47/1.60 % (2321918)------------------------------
% 5.47/1.60 % (2321918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.60 % (2321918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.60 % (2321918)CaDiCaL version: 2.1.3
% 5.47/1.60 % (2321918)Termination reason: Instruction limit
% 5.47/1.60 % (2321918)Termination phase: Saturation
% 5.47/1.60 % (2321918)Time elapsed: 0.133 s
% 5.47/1.60 % (2321918)Peak memory usage: 89 MB
% 5.47/1.60 % (2321918)Instructions burned: 136 (million)
% 5.47/1.60 % (2321920)Instruction limit reached!
% 5.47/1.60 % (2321920)------------------------------
% 5.47/1.60 % (2321920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.60 % (2321920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.60 % (2321920)CaDiCaL version: 2.1.3
% 5.47/1.60 % (2321920)Termination reason: Instruction limit
% 5.47/1.60 % (2321920)Termination phase: Saturation
% 5.47/1.60 % (2321920)Time elapsed: 0.253 s
% 5.47/1.60 % (2321920)Peak memory usage: 90 MB
% 5.47/1.60 % (2321920)Instructions burned: 258 (million)
% 5.47/1.60 % (2321929)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2875619498:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 5.47/1.60 % (2321921)Refutation found. Thanks to Tanya!
% 5.47/1.60 % SZS status Unsatisfiable for theBenchmark
% 0.30/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/1.60 % (2321921)------------------------------
% 0.30/1.60 % (2321921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.60 % (2321921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.60 % (2321921)CaDiCaL version: 2.1.3
% 0.30/1.60 % (2321921)Termination reason: Refutation
% 0.30/1.60 % (2321921)Time elapsed: 0.012 s
% 0.30/1.60 % (2321921)Peak memory usage: 88 MB
% 0.30/1.60 % (2321921)Instructions burned: 10 (million)
% 0.30/1.60 % (2321921)------------------------------
% 0.30/1.60 % (2321921)------------------------------
% 0.30/1.60 % (2321910)Success in time 0.679 s
% 0.30/1.60 % Vampire exiting
%------------------------------------------------------------------------------