%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW410-1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:30:17 PM UTC 2026
% Result : Unsatisfiable 7.74s 1.85s
% Output : Refutation 7.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 38 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_commutative) ).
fof(f2,axiom,
! [X0,X1] : sep(lseg(X0,X0),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ heap(sep(next(X0,X1),sep(lseg(X1,X2),X3)))
| X0 = X1
| heap(sep(lseg(X0,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ heap(sep(lseg(X0,X1),sep(lseg(X1,nil),X2)))
| heap(sep(lseg(X0,nil),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_3) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X4] :
( ~ heap(sep(lseg(X0,X1),sep(lseg(X1,X2),sep(lseg(X2,X3),X4))))
| X2 = X3
| heap(sep(lseg(X0,X2),sep(lseg(X2,X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_5) ).
fof(f15,axiom,
x1 != x3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).
fof(f18,axiom,
heap(sep(lseg(x2,x1),sep(lseg(x3,nil),sep(next(x1,x3),emp)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_5) ).
fof(f19,negated_conjecture,
~ heap(sep(lseg(x3,nil),sep(lseg(x2,x3),emp))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_1) ).
fof(f36,plain,
~ heap(sep(lseg(x2,x3),sep(lseg(x3,nil),emp))),
inference(superposition,[],[f19,f1]) ).
fof(f88,plain,
heap(sep(lseg(x2,x1),sep(next(x1,x3),sep(lseg(x3,nil),emp)))),
inference(superposition,[],[f18,f1]) ).
fof(f89,plain,
heap(sep(next(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp)))),
inference(forward_demodulation,[],[f88,f1]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( ~ heap(sep(lseg(X3,X1),sep(X0,sep(lseg(X1,nil),X2))))
| heap(sep(lseg(X3,nil),sep(X0,X2))) ),
inference(superposition,[],[f10,f1]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ heap(sep(lseg(X0,nil),sep(lseg(X1,X0),X2)))
| heap(sep(lseg(X1,nil),X2)) ),
inference(superposition,[],[f10,f1]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ heap(sep(next(X1,X2),X0))
| X1 = X2
| heap(sep(lseg(X1,X2),X0)) ),
inference(superposition,[],[f9,f2]) ).
fof(f207,plain,
( x1 = x3
| heap(sep(lseg(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp)))) ),
inference(resolution,[],[f202,f89]) ).
fof(f210,plain,
heap(sep(lseg(x1,x3),sep(lseg(x2,x1),sep(lseg(x3,nil),emp)))),
inference(forward_subsumption_resolution,[],[f207,f15]) ).
fof(f602,plain,
! [X2,X3,X0,X1,X4] :
( ~ heap(sep(lseg(X0,X1),sep(lseg(X2,X0),sep(lseg(X1,X3),X4))))
| X1 = X3
| heap(sep(lseg(X2,X1),sep(lseg(X1,X3),X4))) ),
inference(superposition,[],[f12,f1]) ).
fof(f616,plain,
heap(sep(lseg(x1,nil),sep(lseg(x2,x1),emp))),
inference(resolution,[],[f192,f210]) ).
fof(f627,plain,
heap(sep(lseg(x2,nil),emp)),
inference(resolution,[],[f616,f195]) ).
fof(f1905,plain,
( nil = x3
| heap(sep(lseg(x2,x3),sep(lseg(x3,nil),emp))) ),
inference(resolution,[],[f602,f210]) ).
fof(f1914,plain,
nil = x3,
inference(forward_subsumption_resolution,[],[f1905,f36]) ).
fof(f1923,plain,
~ heap(sep(lseg(x2,x3),sep(lseg(x3,x3),emp))),
inference(backward_demodulation,[],[f36,f1914]) ).
fof(f1945,plain,
heap(sep(lseg(x2,x3),emp)),
inference(backward_demodulation,[],[f627,f1914]) ).
fof(f1983,plain,
~ heap(sep(lseg(x2,x3),emp)),
inference(forward_demodulation,[],[f1923,f2]) ).
fof(f1989,plain,
$false,
inference(forward_subsumption_resolution,[],[f1983,f1945]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW410-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n011.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 13:50:31 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 6.37/1.66 % (3393456)Input is clausal, will run a generic CNF schedule.
% 6.37/1.66 % (3393463)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=981129185:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.37/1.66 % (3393465)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3886774574:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.37/1.66 % (3393467)dis-21_1_sil=8000:lcm=predicate:random_seed=1550130111: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)
% 6.37/1.66 % (3393464)lrs+10_1_sil=8000:sp=occurrence:random_seed=2839696102:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.37/1.66 % (3393462)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=113139437:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.37/1.66 % (3393461)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=388935665:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.37/1.66 % (3393466)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=321386837:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.37/1.66 % (3393467)Refutation not found, incomplete strategy
% 6.37/1.66 % (3393467)------------------------------
% 6.37/1.66 % (3393467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.37/1.66 % (3393467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.37/1.66 % (3393467)CaDiCaL version: 2.1.3
% 6.37/1.66 % (3393467)Termination reason: Refutation not found, incomplete strategy
% 6.37/1.66 % (3393467)Time elapsed: 0.002 s
% 6.37/1.66 % (3393467)Peak memory usage: 87 MB
% 6.37/1.66 % (3393467)Instructions burned: 2 (million)
% 6.37/1.66 % (3393464)Instruction limit reached!
% 6.37/1.66 % (3393464)------------------------------
% 6.37/1.66 % (3393464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.37/1.66 % (3393464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.37/1.66 % (3393464)CaDiCaL version: 2.1.3
% 6.37/1.66 % (3393464)Termination reason: Instruction limit
% 6.37/1.66 % (3393464)Termination phase: Saturation
% 6.37/1.66 % (3393464)Time elapsed: 0.064 s
% 6.37/1.66 % (3393464)Peak memory usage: 88 MB
% 6.37/1.66 % (3393464)Instructions burned: 109 (million)
% 6.37/1.66 % (3393465)Instruction limit reached!
% 6.37/1.66 % (3393465)------------------------------
% 6.37/1.66 % (3393465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.37/1.66 % (3393465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.37/1.66 % (3393465)CaDiCaL version: 2.1.3
% 6.37/1.66 % (3393465)Termination reason: Instruction limit
% 6.37/1.66 % (3393465)Termination phase: Saturation
% 6.37/1.66 % (3393465)Time elapsed: 0.071 s
% 6.37/1.66 % (3393465)Peak memory usage: 88 MB
% 6.37/1.66 % (3393465)Instructions burned: 116 (million)
% 6.37/1.66 % (3393466)Instruction limit reached!
% 6.37/1.66 % (3393466)------------------------------
% 6.37/1.66 % (3393466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.37/1.66 % (3393466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.37/1.66 % (3393466)CaDiCaL version: 2.1.3
% 6.37/1.66 % (3393466)Termination reason: Instruction limit
% 6.37/1.66 % (3393466)Termination phase: Saturation
% 6.37/1.66 % (3393466)Time elapsed: 0.101 s
% 6.37/1.66 % (3393466)Peak memory usage: 89 MB
% 6.37/1.66 % (3393466)Instructions burned: 180 (million)
% 6.37/1.66 % (3393475)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=2089880234:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.37/1.66 % (3393476)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2876338334: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)
% 6.37/1.66 % (3393475)Refutation not found, incomplete strategy
% 6.37/1.66 % (3393475)------------------------------
% 6.37/1.66 % (3393475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.37/1.66 % (3393475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.37/1.66 % (3393475)CaDiCaL version: 2.1.3
% 7.74/1.85 % (3393475)Termination reason: Refutation not found, incomplete strategy
% 7.74/1.85 % (3393475)Time elapsed: 0.002 s
% 7.74/1.85 % (3393475)Peak memory usage: 88 MB
% 7.74/1.85 % (3393475)Instructions burned: 1 (million)
% 7.74/1.85 % (3393467)------------------------------
% 7.74/1.85 % (3393467)------------------------------
% 7.74/1.85 % (3393477)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2069286958:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 7.74/1.85 % (3393477)Refutation not found, incomplete strategy
% 7.74/1.85 % (3393477)------------------------------
% 7.74/1.85 % (3393477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.74/1.85 % (3393477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.74/1.85 % (3393477)CaDiCaL version: 2.1.3
% 7.74/1.85 % (3393477)Termination reason: Refutation not found, incomplete strategy
% 7.74/1.85 % (3393477)Time elapsed: 0.001 s
% 7.74/1.85 % (3393477)Peak memory usage: 88 MB
% 7.74/1.85 % (3393477)Instructions burned: 1 (million)
% 7.74/1.85 % (3393476)Instruction limit reached!
% 7.74/1.85 % (3393476)------------------------------
% 7.74/1.85 % (3393476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.74/1.85 % (3393476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.74/1.85 % (3393476)CaDiCaL version: 2.1.3
% 7.74/1.85 % (3393476)Termination reason: Instruction limit
% 7.74/1.85 % (3393476)Termination phase: Saturation
% 7.74/1.85 % (3393476)Time elapsed: 0.119 s
% 7.74/1.85 % (3393476)Peak memory usage: 90 MB
% 7.74/1.85 % (3393476)Instructions burned: 189 (million)
% 7.74/1.85 % (3393481)lrs+10_64_to=lpo:sil=8000:random_seed=1852158542:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 7.74/1.85 % (3393475)------------------------------
% 7.74/1.85 % (3393475)------------------------------
% 7.74/1.85 % (3393477)------------------------------
% 7.74/1.85 % (3393477)------------------------------
% 7.74/1.85 % (3393481)Instruction limit reached!
% 7.74/1.85 % (3393481)------------------------------
% 7.74/1.85 % (3393481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.74/1.85 % (3393481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.74/1.85 % (3393481)CaDiCaL version: 2.1.3
% 7.74/1.85 % (3393481)Termination reason: Instruction limit
% 7.74/1.85 % (3393481)Termination phase: Saturation
% 7.74/1.85 % (3393481)Time elapsed: 0.072 s
% 7.74/1.85 % (3393481)Peak memory usage: 88 MB
% 7.74/1.85 % (3393481)Instructions burned: 127 (million)
% 7.74/1.85 % (3393482)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=610629841:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 7.74/1.85 % (3393482)First to succeed.
% 7.74/1.85 % (3393482)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3393456"
% 7.74/1.85 % (3393484)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3395478063:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 7.74/1.85 % (3393485)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3211890654:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 7.74/1.85 % (3393486)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3520771334:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 7.74/1.85 % (3393486)Instruction limit reached!
% 7.74/1.85 % (3393486)------------------------------
% 7.74/1.85 % (3393486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.74/1.85 % (3393486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.74/1.85 % (3393486)CaDiCaL version: 2.1.3
% 7.74/1.85 % (3393486)Termination reason: Instruction limit
% 7.74/1.85 % (3393486)Termination phase: Saturation
% 7.74/1.85 % (3393486)Time elapsed: 0.062 s
% 7.74/1.85 % (3393486)Peak memory usage: 89 MB
% 7.74/1.85 % (3393486)Instructions burned: 106 (million)
% 7.74/1.85 % (3393484)Instruction limit reached!
% 7.74/1.85 % (3393484)------------------------------
% 7.74/1.85 % (3393484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.74/1.85 % (3393484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.74/1.85 % (3393484)CaDiCaL version: 2.1.3
% 7.74/1.85 % (3393484)Termination reason: Instruction limit
% 7.74/1.85 % (3393484)Termination phase: Saturation
% 7.74/1.85 % (3393484)Time elapsed: 0.098 s
% 7.74/1.85 % (3393484)Peak memory usage: 90 MB
% 7.74/1.85 % (3393484)Instructions burned: 159 (million)
% 7.74/1.85 % (3393482)Refutation found. Thanks to Tanya!
% 7.74/1.85 % SZS status Unsatisfiable for theBenchmark
% 7.74/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 7.74/1.85 % (3393482)------------------------------
% 7.74/1.85 % (3393482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.74/1.85 % (3393482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.74/1.85 % (3393482)CaDiCaL version: 2.1.3
% 7.74/1.85 % (3393482)Termination reason: Refutation
% 7.74/1.85 % (3393482)Time elapsed: 0.077 s
% 7.74/1.85 % (3393482)Peak memory usage: 89 MB
% 7.74/1.85 % (3393482)Instructions burned: 124 (million)
% 7.74/1.85 % (3393482)------------------------------
% 7.74/1.85 % (3393482)------------------------------
% 7.74/1.85 % (3393456)Success in time 1.007 s
% 7.74/1.85 % Vampire exiting
%------------------------------------------------------------------------------