%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:47:58 PM UTC 2026
% Result : Theorem 2.08s 6.32s
% Output : Refutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 4 unt; 0 def)
% Number of atoms : 232 ( 28 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 311 ( 127 ~; 134 |; 39 &)
% ( 6 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 76 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> ! [X1] :
~ ( subset(X1,relation_field(X0))
& X1 != empty_set
& ! [X2] :
~ ( in(X2,X1)
& disjoint(fiber(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
~ ( subset(X2,X1)
& X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& disjoint(fiber(X0,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
fof(f34,conjecture,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f41,plain,
? [X0] :
( ( well_founded_relation(X0)
<~> is_well_founded_in(X0,relation_field(X0)) )
& relation(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f42,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> ! [X1] :
( ~ subset(X1,relation_field(X0))
| empty_set = X1
| ? [X2] :
( in(X2,X1)
& disjoint(fiber(X0,X2),X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
( ~ subset(X2,X1)
| empty_set = X2
| ? [X3] :
( in(X3,X2)
& disjoint(fiber(X0,X3),X2) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
? [X0] :
( ( ~ is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0) )
& ( is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f41]) ).
fof(f52,plain,
? [X0] :
( ( ~ is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0) )
& ( is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0) )
& relation(X0) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
( ( ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ well_founded_relation(sK0) )
& ( is_well_founded_in(sK0,relation_field(sK0))
| well_founded_relation(sK0) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f52]) ).
fof(f54,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ? [X1] :
( subset(X1,relation_field(X0))
& empty_set != X1
& ! [X2] :
( ~ in(X2,X1)
| ~ disjoint(fiber(X0,X2),X1) ) ) )
& ( ! [X1] :
( ~ subset(X1,relation_field(X0))
| empty_set = X1
| ? [X2] :
( in(X2,X1)
& disjoint(fiber(X0,X2),X1) ) )
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f55,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ? [X1] :
( subset(X1,relation_field(X0))
& empty_set != X1
& ! [X2] :
( ~ in(X2,X1)
| ~ disjoint(fiber(X0,X2),X1) ) ) )
& ( ! [X3] :
( ~ subset(X3,relation_field(X0))
| empty_set = X3
| ? [X4] :
( in(X4,X3)
& disjoint(fiber(X0,X4),X3) ) )
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ( subset(sK1(X0),relation_field(X0))
& empty_set != sK1(X0)
& ! [X2] :
( ~ in(X2,sK1(X0))
| ~ disjoint(fiber(X0,X2),sK1(X0)) ) ) )
& ( ! [X3] :
( ~ subset(X3,relation_field(X0))
| empty_set = X3
| ( in(sK2(X0,X3),X3)
& disjoint(fiber(X0,sK2(X0,X3)),X3) ) )
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X4,sK2(X0,X3))],[f55]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( is_well_founded_in(X0,X1)
| ? [X2] :
( subset(X2,X1)
& empty_set != X2
& ! [X3] :
( ~ in(X3,X2)
| ~ disjoint(fiber(X0,X3),X2) ) ) )
& ( ! [X2] :
( ~ subset(X2,X1)
| empty_set = X2
| ? [X3] :
( in(X3,X2)
& disjoint(fiber(X0,X3),X2) ) )
| ~ is_well_founded_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( is_well_founded_in(X0,X1)
| ? [X2] :
( subset(X2,X1)
& empty_set != X2
& ! [X3] :
( ~ in(X3,X2)
| ~ disjoint(fiber(X0,X3),X2) ) ) )
& ( ! [X4] :
( ~ subset(X4,X1)
| empty_set = X4
| ? [X5] :
( in(X5,X4)
& disjoint(fiber(X0,X5),X4) ) )
| ~ is_well_founded_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( is_well_founded_in(X0,X1)
| ( subset(sK3(X0,X1),X1)
& empty_set != sK3(X0,X1)
& ! [X3] :
( ~ in(X3,sK3(X0,X1))
| ~ disjoint(fiber(X0,X3),sK3(X0,X1)) ) ) )
& ( ! [X4] :
( ~ subset(X4,X1)
| empty_set = X4
| ( in(sK4(X0,X4),X4)
& disjoint(fiber(X0,sK4(X0,X4)),X4) ) )
| ~ is_well_founded_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3(X0,X1)),skolemize(X5,sK4(X0,X4))],[f58]) ).
fof(f62,plain,
relation(sK0),
inference(cnf_transformation,[],[f53]) ).
fof(f63,plain,
( is_well_founded_in(sK0,relation_field(sK0))
| well_founded_relation(sK0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f64,plain,
( ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ well_founded_relation(sK0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f65,plain,
! [X3,X0] :
( disjoint(fiber(X0,sK2(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f66,plain,
! [X3,X0] :
( in(sK2(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f67,plain,
! [X2,X0] :
( ~ disjoint(fiber(X0,X2),sK1(X0))
| ~ in(X2,sK1(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f68,plain,
! [X0] :
( empty_set != sK1(X0)
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f69,plain,
! [X0] :
( subset(sK1(X0),relation_field(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f70,plain,
! [X0,X1,X4] :
( disjoint(fiber(X0,sK4(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f71,plain,
! [X0,X1,X4] :
( in(sK4(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f72,plain,
! [X3,X0,X1] :
( ~ disjoint(fiber(X0,X3),sK3(X0,X1))
| ~ in(X3,sK3(X0,X1))
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f73,plain,
! [X0,X1] :
( empty_set != sK3(X0,X1)
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f74,plain,
! [X0,X1] :
( subset(sK3(X0,X1),X1)
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f139,plain,
! [X0,X1] :
( empty_set = sK3(X0,X1)
| ~ subset(sK3(X0,X1),relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ in(sK2(X0,sK3(X0,X1)),sK3(X0,X1))
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(resolution,[],[f65,f72]) ).
fof(f140,plain,
! [X0,X1] :
( empty_set = sK3(X0,X1)
| ~ subset(sK3(X0,X1),relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ in(sK2(X0,sK3(X0,X1)),sK3(X0,X1))
| is_well_founded_in(X0,X1) ),
inference(duplicate_literal_removal,[],[f139]) ).
fof(f142,plain,
! [X0,X1] :
( empty_set = sK3(X0,X1)
| ~ subset(sK3(X0,X1),relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0)
| is_well_founded_in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f140,f66]) ).
fof(f143,plain,
! [X0,X1] :
( ~ subset(sK3(X0,X1),relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0)
| is_well_founded_in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f142,f73]) ).
fof(f144,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ relation(X0)
| is_well_founded_in(X0,relation_field(X0))
| is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(resolution,[],[f143,f74]) ).
fof(f145,plain,
! [X0] :
( is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0)
| ~ well_founded_relation(X0) ),
inference(duplicate_literal_removal,[],[f144]) ).
fof(f146,plain,
( ~ relation(sK0)
| ~ well_founded_relation(sK0)
| ~ well_founded_relation(sK0) ),
inference(resolution,[],[f145,f64]) ).
fof(f147,plain,
( ~ relation(sK0)
| ~ well_founded_relation(sK0) ),
inference(duplicate_literal_removal,[],[f146]) ).
fof(f148,plain,
~ well_founded_relation(sK0),
inference(forward_subsumption_resolution,[],[f147,f62]) ).
fof(f149,plain,
! [X0,X1] :
( empty_set = sK1(X0)
| ~ subset(sK1(X0),X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0)
| ~ in(sK4(X0,sK1(X0)),sK1(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(resolution,[],[f70,f67]) ).
fof(f152,plain,
! [X0,X1] :
( empty_set = sK1(X0)
| ~ subset(sK1(X0),X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0)
| ~ in(sK4(X0,sK1(X0)),sK1(X0))
| well_founded_relation(X0) ),
inference(duplicate_literal_removal,[],[f149]) ).
fof(f154,plain,
! [X0,X1] :
( empty_set = sK1(X0)
| ~ subset(sK1(X0),X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0)
| well_founded_relation(X0) ),
inference(forward_subsumption_resolution,[],[f152,f71]) ).
fof(f156,plain,
! [X0,X1] :
( ~ subset(sK1(X0),X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0)
| well_founded_relation(X0) ),
inference(forward_subsumption_resolution,[],[f154,f68]) ).
fof(f157,plain,
! [X0] :
( ~ is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0)
| well_founded_relation(X0)
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(resolution,[],[f156,f69]) ).
fof(f159,plain,
! [X0] :
( ~ is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0)
| well_founded_relation(X0) ),
inference(duplicate_literal_removal,[],[f157]) ).
fof(f160,plain,
( ~ relation(sK0)
| well_founded_relation(sK0)
| well_founded_relation(sK0) ),
inference(resolution,[],[f159,f63]) ).
fof(f163,plain,
( ~ relation(sK0)
| well_founded_relation(sK0) ),
inference(duplicate_literal_removal,[],[f160]) ).
fof(f164,plain,
well_founded_relation(sK0),
inference(forward_subsumption_resolution,[],[f163,f62]) ).
fof(f165,plain,
$false,
inference(forward_subsumption_resolution,[],[f164,f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.40 % Computer : n017.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.04/5.40 % CPULimit : 300
% 0.04/5.40 % WCLimit : 300
% 0.04/5.40 % DateTime : Mon Sep 28 04:12:12 UTC 2026
% 0.04/5.40 % CPUTime :
% 0.04/5.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/5.43 Running first-order theorem proving
% 0.04/5.43 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
% 2.08/6.32 % (3193026)Detected formulas, will run a generic FOF schedule.
% 2.08/6.32 % (3193033)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=1556853875:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.08/6.32 % (3193031)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=1402841909:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.08/6.32 % (3193036)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1607220924:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.08/6.32 % (3193032)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=947380537:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.08/6.32 % (3193037)dis-21_1_sil=8000:lcm=predicate:random_seed=3996400500: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)
% 2.08/6.32 % (3193034)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4151109510:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.08/6.32 % (3193035)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1855426561:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.08/6.32 % (3193034)Refutation not found, incomplete strategy
% 2.08/6.32 % (3193034)------------------------------
% 2.08/6.32 % (3193034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.08/6.32 % (3193034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.08/6.32 % (3193034)CaDiCaL version: 2.1.3
% 2.08/6.32 % (3193034)Termination reason: Refutation not found, incomplete strategy
% 2.08/6.32 % (3193034)Time elapsed: 0.002 s
% 2.08/6.32 % (3193034)Peak memory usage: 88 MB
% 2.08/6.32 % (3193034)Instructions burned: 1 (million)
% 2.08/6.32 % (3193035)First to succeed.
% 2.08/6.32 % (3193035)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3193026"
% 2.08/6.32 % (3193036)Also succeeded, but the first one will report.
% 2.08/6.32 % (3193037)Instruction limit reached!
% 2.08/6.32 % (3193037)------------------------------
% 2.08/6.32 % (3193037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.08/6.32 % (3193037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.08/6.32 % (3193037)CaDiCaL version: 2.1.3
% 2.08/6.32 % (3193037)Termination reason: Instruction limit
% 2.08/6.32 % (3193037)Termination phase: Saturation
% 2.08/6.32 % (3193037)Time elapsed: 0.084 s
% 2.08/6.32 % (3193037)Peak memory usage: 89 MB
% 2.08/6.32 % (3193037)Instructions burned: 131 (million)
% 2.08/6.32 % (3193034)------------------------------
% 2.08/6.32 % (3193034)------------------------------
% 2.08/6.32 % (3193035)Refutation found. Thanks to Tanya!
% 2.08/6.32 % SZS status Theorem for theBenchmark
% 2.08/6.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.08/6.41 % (3193035)------------------------------
% 2.08/6.41 % (3193035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.08/6.41 % (3193035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.08/6.41 % (3193035)CaDiCaL version: 2.1.3
% 2.08/6.41 % (3193035)Termination reason: Refutation
% 2.08/6.41 % (3193035)Time elapsed: 0.005 s
% 2.08/6.41 % (3193035)Peak memory usage: 88 MB
% 2.08/6.41 % (3193035)Instructions burned: 5 (million)
% 2.08/6.41 % (3193035)------------------------------
% 2.08/6.41 % (3193035)------------------------------
% 2.08/6.41 % (3193026)Success in time 0.437 s
% 2.08/6.41 % Vampire exiting
%------------------------------------------------------------------------------