%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL274-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 11:51:50 AM UTC 2026
% Result : Unsatisfiable 5.31s 1.88s
% Output : Refutation 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 24 unt; 3 def)
% Number of atoms : 103 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 96 ( 50 ~; 43 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f4,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f6,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
fof(f7,axiom,
! [X0] :
( theorem(X0)
| ~ axiom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
fof(f8,axiom,
! [X0,X1] :
( theorem(X0)
| ~ theorem(implies(X1,X0))
| ~ theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f9,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
fof(f10,axiom,
! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f11,negated_conjecture,
~ theorem(equivalent(or(p,q),or(q,p))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f12,plain,
! [X0,X1] : equivalent(X0,X1) = not(or(not(or(not(X0),X1)),not(or(not(X1),X0)))),
inference(definition_unfolding,[],[f10,f9,f6,f6]) ).
fof(f13,plain,
~ theorem(not(or(not(or(not(or(p,q)),or(q,p))),not(or(not(or(q,p)),or(p,q)))))),
inference(definition_unfolding,[],[f11,f12]) ).
fof(f14,plain,
! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f5,f6,f6,f6]) ).
fof(f15,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f16,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f17,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f18,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f19,plain,
! [X0,X1] :
( ~ theorem(or(not(X1),X0))
| theorem(X0)
| ~ theorem(X1) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f21,plain,
! [X0,X1] :
( ~ axiom(or(not(X1),X0))
| ~ theorem(X1)
| theorem(X0) ),
inference(resolution,[],[f19,f7]) ).
fof(f23,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[],[f21,f18]) ).
fof(f24,plain,
! [X0,X1] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f21,f16]) ).
fof(f25,plain,
! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f21,f15]) ).
fof(f26,plain,
! [X2,X0,X1] :
( theorem(or(not(or(X2,X0)),or(X2,X1)))
| ~ theorem(or(not(X0),X1)) ),
inference(resolution,[],[f14,f21]) ).
fof(f30,plain,
! [X0,X1] :
( ~ theorem(or(X0,not(X1)))
| theorem(X0)
| ~ theorem(X1) ),
inference(resolution,[],[f24,f19]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ theorem(or(X0,or(not(X1),X2)))
| theorem(or(X0,X2))
| ~ theorem(X1) ),
inference(resolution,[],[f25,f19]) ).
fof(f43,plain,
! [X0,X1] :
( ~ theorem(or(X0,or(or(X0,X1),X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f25,f23]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ),
inference(resolution,[],[f26,f19]) ).
fof(f54,plain,
! [X0,X1] :
( ~ axiom(or(X0,or(or(X0,X1),X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f43,f7]) ).
fof(f58,plain,
! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),X2))
| ~ theorem(X0)
| ~ theorem(or(not(X1),X2)) ),
inference(resolution,[],[f42,f26]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ axiom(or(not(X2),X1))
| ~ theorem(or(X0,X2))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f49,f7]) ).
fof(f94,plain,
! [X0] : theorem(or(not(X0),X0)),
inference(resolution,[],[f54,f17]) ).
fof(f124,plain,
! [X2,X0,X1] :
( theorem(or(X0,or(X2,X1)))
| ~ theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f65,f16]) ).
fof(f139,plain,
! [X2,X0,X1] :
( theorem(not(or(not(X0),X1)))
| ~ theorem(or(not(X1),not(X2)))
| ~ theorem(X0)
| ~ theorem(X2) ),
inference(resolution,[],[f58,f30]) ).
fof(f699,plain,
! [X0] :
( ~ theorem(or(not(not(or(not(or(q,p)),or(p,q)))),not(X0)))
| ~ theorem(or(not(or(p,q)),or(q,p)))
| ~ theorem(X0) ),
inference(resolution,[],[f139,f13]) ).
fof(f705,definition,
( spl0_27
<=> theorem(or(not(or(p,q)),or(q,p))) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f706,plain,
( ~ theorem(or(not(or(p,q)),or(q,p)))
| spl0_27 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f708,definition,
( spl0_28
<=> ! [X0] :
( ~ theorem(or(not(not(or(not(or(q,p)),or(p,q)))),not(X0)))
| ~ theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f709,plain,
( ! [X0] :
( ~ theorem(or(not(not(or(not(or(q,p)),or(p,q)))),not(X0)))
| ~ theorem(X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f710,plain,
( ~ spl0_27
| spl0_28 ),
inference(avatar_split_clause,[],[f699,f708,f705]) ).
fof(f715,plain,
( ~ theorem(or(not(or(p,q)),or(p,q)))
| spl0_27 ),
inference(resolution,[],[f706,f124]) ).
fof(f728,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f715,f94]) ).
fof(f729,plain,
spl0_27,
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f778,plain,
( ~ theorem(or(not(or(q,p)),or(p,q)))
| ~ spl0_28 ),
inference(resolution,[],[f709,f94]) ).
fof(f801,definition,
( spl0_37
<=> theorem(or(not(or(q,p)),or(p,q))) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f802,plain,
( ~ theorem(or(not(or(q,p)),or(p,q)))
| spl0_37 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f804,plain,
( ~ spl0_37
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f778,f708,f801]) ).
fof(f818,plain,
( ~ theorem(or(not(or(q,p)),or(q,p)))
| spl0_37 ),
inference(resolution,[],[f802,f124]) ).
fof(f831,plain,
( $false
| spl0_37 ),
inference(forward_subsumption_resolution,[],[f818,f94]) ).
fof(f832,plain,
spl0_37,
inference(avatar_contradiction_clause,[],[f831]) ).
cnf(s47,plain,
( ~ spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f710]) ).
cnf(s49,plain,
spl0_27,
inference(sat_conversion,[],[f729]) ).
cnf(s60,plain,
( ~ spl0_28
| ~ spl0_37 ),
inference(sat_conversion,[],[f804]) ).
cnf(s62,plain,
spl0_37,
inference(sat_conversion,[],[f832]) ).
cnf(s63,plain,
~ spl0_28,
inference(rat,[],[s60,s62]) ).
cnf(s64,plain,
$false,
inference(rat,[],[s47,s63,s49]) ).
fof(f833,plain,
$false,
inference(avatar_sat_refutation,[],[s64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL274-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n010.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 15:32:47 UTC 2026
% 0.16/0.39 % CPUTime :
% 0.16/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 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
% 1.60/1.69 % (1103685)Input is clausal, will run a generic CNF schedule.
% 1.60/1.69 % (1103709)lrs+10_1_sil=8000:sp=occurrence:random_seed=1591331783:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.60/1.69 % (1103712)dis-21_1_sil=8000:lcm=predicate:random_seed=2860178661: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)
% 1.60/1.69 % (1103707)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2863423301:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.60/1.69 % (1103708)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2592877393:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.60/1.69 % (1103705)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=99141261:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.60/1.69 % (1103709)Instruction limit reached!
% 1.60/1.69 % (1103709)------------------------------
% 1.60/1.69 % (1103709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.60/1.69 % (1103709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.60/1.69 % (1103709)CaDiCaL version: 2.1.3
% 1.60/1.69 % (1103709)Termination reason: Instruction limit
% 1.60/1.69 % (1103709)Termination phase: Saturation
% 1.60/1.69 % (1103709)Time elapsed: 0.059 s
% 1.60/1.69 % (1103709)Peak memory usage: 89 MB
% 1.60/1.69 % (1103709)Instructions burned: 108 (million)
% 1.60/1.69 % (1103712)Instruction limit reached!
% 1.60/1.69 % (1103712)------------------------------
% 1.60/1.69 % (1103712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.60/1.69 % (1103712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.60/1.69 % (1103712)CaDiCaL version: 2.1.3
% 1.60/1.69 % (1103712)Termination reason: Instruction limit
% 1.60/1.69 % (1103712)Termination phase: Saturation
% 1.60/1.69 % (1103712)Time elapsed: 0.065 s
% 1.60/1.69 % (1103712)Peak memory usage: 88 MB
% 1.60/1.69 % (1103712)Instructions burned: 121 (million)
% 1.60/1.69 % (1103710)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=442378127:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.60/1.69 % (1103711)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3883164490:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.60/1.69 % (1103710)First to succeed.
% 1.60/1.69 % (1103710)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1103685"
% 1.60/1.69 % (1103720)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2951112589: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)
% 1.60/1.69 % (1103720)Refutation not found, incomplete strategy
% 1.60/1.69 % (1103720)------------------------------
% 1.60/1.69 % (1103720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.60/1.69 % (1103720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.60/1.69 % (1103720)CaDiCaL version: 2.1.3
% 1.60/1.69 % (1103720)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.69 % (1103720)Time elapsed: 0.002 s
% 1.60/1.69 % (1103720)Peak memory usage: 87 MB
% 1.60/1.69 % (1103711)Instruction limit reached!
% 1.60/1.69 % (1103711)------------------------------
% 1.60/1.69 % (1103711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.60/1.69 % (1103711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.60/1.69 % (1103711)CaDiCaL version: 2.1.3
% 1.60/1.69 % (1103711)Termination reason: Instruction limit
% 1.60/1.69 % (1103711)Termination phase: Saturation
% 1.60/1.69 % (1103711)Time elapsed: 0.185 s
% 1.60/1.69 % (1103711)Peak memory usage: 89 MB
% 1.60/1.69 % (1103711)Instructions burned: 180 (million)
% 1.60/1.69 % (1103719)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=1876966066:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.60/1.69 % (1103719)Refutation not found, incomplete strategy
% 1.60/1.69 % (1103719)------------------------------
% 1.60/1.69 % (1103719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.60/1.69 % (1103719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.88 % (1103719)CaDiCaL version: 2.1.3
% 5.31/1.88 % (1103719)Termination reason: Refutation not found, incomplete strategy
% 5.31/1.88 % (1103719)Time elapsed: 0.002 s
% 5.31/1.88 % (1103719)Peak memory usage: 88 MB
% 5.31/1.88 % (1103728)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2205247920:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 5.31/1.88 % (1103728)Refutation not found, incomplete strategy
% 5.31/1.88 % (1103728)------------------------------
% 5.31/1.88 % (1103728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.88 % (1103728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.88 % (1103728)CaDiCaL version: 2.1.3
% 5.31/1.88 % (1103728)Termination reason: Refutation not found, incomplete strategy
% 5.31/1.88 % (1103728)Time elapsed: 0.001 s
% 5.31/1.88 % (1103728)Peak memory usage: 88 MB
% 5.31/1.88 % (1103710)Refutation found. Thanks to Tanya!
% 5.31/1.88 % SZS status Unsatisfiable for theBenchmark
% 5.31/1.88 % SZS output start Proof for theBenchmark
% See solution above
% 5.31/1.88 % (1103710)------------------------------
% 5.31/1.88 % (1103710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.88 % (1103710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.88 % (1103710)CaDiCaL version: 2.1.3
% 5.31/1.88 % (1103710)Termination reason: Refutation
% 5.31/1.88 % (1103710)Time elapsed: 0.027 s
% 5.31/1.88 % (1103710)Peak memory usage: 89 MB
% 5.31/1.88 % (1103710)Instructions burned: 23 (million)
% 5.31/1.88 % (1103710)------------------------------
% 5.31/1.88 % (1103710)------------------------------
% 5.31/1.88 % (1103685)Success in time 0.643 s
% 5.31/1.88 % Vampire exiting
%------------------------------------------------------------------------------