%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC025-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 01:02:05 PM UTC 2026
% Result : Unsatisfiable 3.84s 1.52s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 52 ( 10 unt; 2 def)
% Number of atoms : 128 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 147 ( 71 ~; 74 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
fof(f112,axiom,
! [X0] :
( cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
fof(f149,axiom,
! [X2,X0,X1] :
( X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).
fof(f200,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
fof(f201,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f207,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| memberP(sk4,X0)
| ~ memberP(sk3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| memberP(sk3,X0)
| ~ memberP(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( nil = sk2
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f212,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f222,plain,
! [X2,X1] :
( ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f149]) ).
fof(f239,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(duplicate_literal_removal,[],[f222]) ).
fof(f244,definition,
( spl0_1
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f245,plain,
( nil = sk2
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f246,plain,
( nil != sk2
| spl0_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl0_2
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f249,plain,
( nil = sk1
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f250,plain,
( nil != sk1
| spl0_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f212,f248,f244]) ).
fof(f252,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f209,f244,f248]) ).
fof(f301,plain,
! [X0] :
( memberP(sk2,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(forward_demodulation,[],[f207,f204]) ).
fof(f302,plain,
! [X0] :
( ~ memberP(sk1,X0)
| memberP(sk2,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f301,f205]) ).
fof(f304,plain,
! [X0] :
( memberP(sk1,X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
inference(forward_demodulation,[],[f208,f205]) ).
fof(f461,plain,
! [X0] :
( memberP(X0,skaf83(X0))
| ~ ssItem(skaf83(X0))
| ~ ssList(skaf82(X0))
| ~ ssList(X0)
| nil = X0 ),
inference(superposition,[],[f239,f112]) ).
fof(f462,plain,
! [X0] :
( memberP(X0,skaf83(X0))
| ~ ssList(skaf82(X0))
| ~ ssList(X0)
| nil = X0 ),
inference(forward_subsumption_resolution,[],[f461,f12]) ).
fof(f464,plain,
! [X0] :
( memberP(X0,skaf83(X0))
| ~ ssList(X0)
| nil = X0 ),
inference(forward_subsumption_resolution,[],[f462,f13]) ).
fof(f699,plain,
! [X0] :
( ~ memberP(sk2,X0)
| memberP(sk1,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f304,f204]) ).
fof(f937,plain,
( ! [X0] :
( memberP(nil,X0)
| ~ memberP(sk1,X0)
| ~ ssItem(X0) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f302,f245]) ).
fof(f938,plain,
( ! [X0] :
( ~ memberP(sk1,X0)
| ~ ssItem(X0) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f937,f71]) ).
fof(f973,plain,
( ~ ssList(sk1)
| nil = sk1
| ~ ssItem(skaf83(sk1))
| ~ spl0_1 ),
inference(resolution,[],[f464,f938]) ).
fof(f978,plain,
( nil = sk1
| ~ ssItem(skaf83(sk1))
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f973,f200]) ).
fof(f980,plain,
( ~ ssItem(skaf83(sk1))
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f978,f250]) ).
fof(f982,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f980,f12]) ).
fof(f983,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f982]) ).
fof(f994,plain,
( ! [X0] :
( memberP(nil,X0)
| ~ memberP(sk2,X0)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f699,f249]) ).
fof(f995,plain,
( ! [X0] :
( ~ memberP(sk2,X0)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f994,f71]) ).
fof(f997,plain,
( ~ ssItem(skaf83(sk2))
| ~ ssList(sk2)
| nil = sk2
| ~ spl0_2 ),
inference(resolution,[],[f995,f464]) ).
fof(f999,plain,
( ~ ssList(sk2)
| nil = sk2
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f997,f12]) ).
fof(f1001,plain,
( nil = sk2
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f999,f201]) ).
fof(f1002,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1001,f246]) ).
fof(f1003,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f1002]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f251]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f252]) ).
cnf(s41,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f983]) ).
cnf(s42,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1003]) ).
cnf(s57,plain,
spl0_1,
inference(rat,[],[s2,s42]) ).
cnf(s58,plain,
spl0_2,
inference(rat,[],[s41,s57]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s1,s58,s57]) ).
fof(f1004,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC025-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 07:32:12 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.84/1.52 % (1407836)Input is clausal, will run a generic CNF schedule.
% 3.84/1.52 % (1407841)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=668882246:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.84/1.52 % (1407844)lrs+10_1_sil=8000:sp=occurrence:random_seed=1203246347:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.84/1.52 % (1407842)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1322869009:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.84/1.52 % (1407845)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3693239956:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.84/1.52 % (1407847)dis-21_1_sil=8000:lcm=predicate:random_seed=534630160: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)
% 3.84/1.52 % (1407843)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2689627941:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.84/1.52 % (1407846)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3872320030:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.84/1.52 % (1407846)First to succeed.
% 3.84/1.52 % (1407846)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1407836"
% 3.84/1.52 % (1407845)Instruction limit reached!
% 3.84/1.52 % (1407845)------------------------------
% 3.84/1.52 % (1407845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.52 % (1407845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.52 % (1407845)CaDiCaL version: 2.1.3
% 3.84/1.52 % (1407845)Termination reason: Instruction limit
% 3.84/1.52 % (1407845)Termination phase: Saturation
% 3.84/1.52 % (1407845)Time elapsed: 0.061 s
% 3.84/1.52 % (1407845)Peak memory usage: 88 MB
% 3.84/1.52 % (1407845)Instructions burned: 115 (million)
% 3.84/1.52 % (1407844)Instruction limit reached!
% 3.84/1.52 % (1407844)------------------------------
% 3.84/1.52 % (1407844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.52 % (1407844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.52 % (1407844)CaDiCaL version: 2.1.3
% 3.84/1.52 % (1407844)Termination reason: Instruction limit
% 3.84/1.52 % (1407844)Termination phase: Saturation
% 3.84/1.52 % (1407844)Time elapsed: 0.065 s
% 3.84/1.52 % (1407844)Peak memory usage: 90 MB
% 3.84/1.52 % (1407844)Instructions burned: 107 (million)
% 3.84/1.52 % (1407847)Instruction limit reached!
% 3.84/1.52 % (1407847)------------------------------
% 3.84/1.52 % (1407847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.52 % (1407847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.52 % (1407847)CaDiCaL version: 2.1.3
% 3.84/1.52 % (1407847)Termination reason: Instruction limit
% 3.84/1.52 % (1407847)Termination phase: Saturation
% 3.84/1.52 % (1407847)Time elapsed: 0.068 s
% 3.84/1.52 % (1407847)Peak memory usage: 90 MB
% 3.84/1.52 % (1407847)Instructions burned: 117 (million)
% 3.84/1.52 % (1407855)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=3893945322:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.84/1.52 % (1407856)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3413858127: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)
% 3.84/1.52 % (1407857)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3442195830:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.84/1.52 % (1407857)Refutation not found, incomplete strategy
% 3.84/1.52 % (1407857)------------------------------
% 3.84/1.52 % (1407857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.52 % (1407857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.52 % (1407857)CaDiCaL version: 2.1.3
% 3.84/1.52 % (1407857)Termination reason: Refutation not found, incomplete strategy
% 3.84/1.52 % (1407857)Time elapsed: 0.003 s
% 3.84/1.52 % (1407857)Peak memory usage: 88 MB
% 3.84/1.52 % (1407857)Instructions burned: 3 (million)
% 3.84/1.52 % (1407855)Refutation not found, incomplete strategy
% 3.84/1.52 % (1407855)------------------------------
% 3.84/1.52 % (1407855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.52 % (1407855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.52 % (1407855)CaDiCaL version: 2.1.3
% 3.84/1.52 % (1407855)Termination reason: Refutation not found, incomplete strategy
% 3.84/1.52 % (1407855)Time elapsed: 0.003 s
% 3.84/1.52 % (1407855)Peak memory usage: 88 MB
% 3.84/1.52 % (1407855)Instructions burned: 3 (million)
% 3.84/1.52 % (1407846)Refutation found. Thanks to Tanya!
% 3.84/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.84/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.52 % (1407846)------------------------------
% 3.84/1.52 % (1407846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.52 % (1407846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.52 % (1407846)CaDiCaL version: 2.1.3
% 3.84/1.52 % (1407846)Termination reason: Refutation
% 3.84/1.52 % (1407846)Time elapsed: 0.024 s
% 3.84/1.52 % (1407846)Peak memory usage: 90 MB
% 3.84/1.52 % (1407846)Instructions burned: 31 (million)
% 3.84/1.52 % (1407846)------------------------------
% 3.84/1.52 % (1407846)------------------------------
% 3.84/1.52 % (1407836)Success in time 0.456 s
% 3.84/1.52 % Vampire exiting
%------------------------------------------------------------------------------