%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV415+2 : 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 : n012.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 01:09:09 PM UTC 2026
% Result : Theorem 1.72s 0.59s
% Output : Refutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 19 unt; 4 def)
% Number of atoms : 99 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 42 ~; 38 |; 5 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 18 con; 0-3 aty)
% Number of variables : 171 ( 0 sgn 134 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f54,axiom,
! [X0,X1] : i(triple(X0,create_slb,X1)) = create_pq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f55,axiom,
! [X0,X1,X2,X3,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f63,axiom,
( ( ! [X0,X1,X2,X3] : i(triple(X0,create_slb,X2)) = i(triple(X1,create_slb,X3))
& ! [X4] :
( ! [X5,X6,X7,X8] : i(triple(X5,X4,X7)) = i(triple(X6,X4,X8))
=> ! [X9,X10,X11,X12,X13,X14] : i(triple(X9,insert_slb(X4,pair(X13,X14)),X11)) = i(triple(X10,insert_slb(X4,pair(X13,X14)),X12)) ) )
=> ! [X15,X16,X17,X18,X19] : i(triple(X15,X17,X18)) = i(triple(X16,X17,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big2_induction) ).
fof(f64,conjecture,
! [X0,X1,X2,X3] : i(insert_cpq(triple(X0,X1,X2),X3)) = insert_pq(i(triple(X0,X1,X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co2) ).
fof(f65,negated_conjecture,
~ ! [X0,X1,X2,X3] : i(insert_cpq(triple(X0,X1,X2),X3)) = insert_pq(i(triple(X0,X1,X2)),X3),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f116,plain,
( ! [X15,X16,X17,X18,X19] : i(triple(X15,X17,X18)) = i(triple(X16,X17,X19))
| ? [X0,X1,X2,X3] : i(triple(X0,create_slb,X2)) != i(triple(X1,create_slb,X3))
| ? [X4] :
( ? [X9,X10,X11,X12,X13,X14] : i(triple(X9,insert_slb(X4,pair(X13,X14)),X11)) != i(triple(X10,insert_slb(X4,pair(X13,X14)),X12))
& ! [X5,X6,X7,X8] : i(triple(X5,X4,X7)) = i(triple(X6,X4,X8)) ) ),
inference(ennf_transformation,[],[f63]) ).
fof(f117,plain,
( ! [X15,X16,X17,X18,X19] : i(triple(X15,X17,X18)) = i(triple(X16,X17,X19))
| ? [X0,X1,X2,X3] : i(triple(X0,create_slb,X2)) != i(triple(X1,create_slb,X3))
| ? [X4] :
( ? [X9,X10,X11,X12,X13,X14] : i(triple(X9,insert_slb(X4,pair(X13,X14)),X11)) != i(triple(X10,insert_slb(X4,pair(X13,X14)),X12))
& ! [X5,X6,X7,X8] : i(triple(X5,X4,X7)) = i(triple(X6,X4,X8)) ) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
? [X0,X1,X2,X3] : insert_pq(i(triple(X0,X1,X2)),X3) != i(insert_cpq(triple(X0,X1,X2),X3)),
inference(ennf_transformation,[],[f65]) ).
fof(f128,plain,
( ! [X0,X1,X2,X3,X4] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4))
| ? [X5,X6,X7,X8] : i(triple(X5,create_slb,X7)) != i(triple(X6,create_slb,X8))
| ? [X9] :
( ? [X10,X11,X12,X13,X14,X15] : i(triple(X10,insert_slb(X9,pair(X14,X15)),X12)) != i(triple(X11,insert_slb(X9,pair(X14,X15)),X13))
& ! [X16,X17,X18,X19] : i(triple(X16,X9,X18)) = i(triple(X17,X9,X19)) ) ),
inference(rectify,[],[f117]) ).
fof(f129,plain,
( ! [X0,X1,X2,X3,X4] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4))
| i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4))
| ( i(triple(sK6,insert_slb(sK5,pair(sK10,sK11)),sK8)) != i(triple(sK7,insert_slb(sK5,pair(sK10,sK11)),sK9))
& ! [X16,X17,X18,X19] : i(triple(X16,sK5,X18)) = i(triple(X17,sK5,X19)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11]),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3),skolemize(X8,sK4),skolemize(X9,sK5),skolemize(X10,sK6),skolemize(X11,sK7),skolemize(X12,sK8),skolemize(X13,sK9),skolemize(X14,sK10),skolemize(X15,sK11)],[f128]) ).
fof(f130,plain,
insert_pq(i(triple(sK12,sK13,sK14)),sK15) != i(insert_cpq(triple(sK12,sK13,sK14),sK15)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f118]) ).
fof(f182,plain,
! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
inference(cnf_transformation,[],[f42]) ).
fof(f194,plain,
! [X0,X1] : create_pq = i(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f195,plain,
! [X2,X3,X0,X1,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3),
inference(cnf_transformation,[],[f55]) ).
fof(f196,plain,
! [X2,X3,X0,X1,X18,X19,X16,X4,X17] :
( i(triple(X0,X2,X3)) = i(triple(X1,X2,X4))
| i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4))
| i(triple(X16,sK5,X18)) = i(triple(X17,sK5,X19)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f197,plain,
! [X2,X3,X0,X1,X4] :
( i(triple(X0,X2,X3)) = i(triple(X1,X2,X4))
| i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4))
| i(triple(sK6,insert_slb(sK5,pair(sK10,sK11)),sK8)) != i(triple(sK7,insert_slb(sK5,pair(sK10,sK11)),sK9)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f198,plain,
insert_pq(i(triple(sK12,sK13,sK14)),sK15) != i(insert_cpq(triple(sK12,sK13,sK14),sK15)),
inference(cnf_transformation,[],[f130]) ).
fof(f204,definition,
( spl16_1
<=> ! [X18,X16,X17,X19] : i(triple(X16,sK5,X18)) = i(triple(X17,sK5,X19)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f205,plain,
( ! [X18,X19,X16,X17] : i(triple(X16,sK5,X18)) = i(triple(X17,sK5,X19))
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,definition,
( spl16_2
<=> i(triple(sK1,create_slb,sK3)) = i(triple(sK2,create_slb,sK4)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f209,plain,
( i(triple(sK1,create_slb,sK3)) != i(triple(sK2,create_slb,sK4))
| spl16_2 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f211,definition,
( spl16_3
<=> ! [X4,X0,X3,X2,X1] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f212,plain,
( ! [X2,X3,X0,X1,X4] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4))
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f213,plain,
( spl16_1
| ~ spl16_2
| spl16_3 ),
inference(avatar_split_clause,[],[f196,f211,f207,f204]) ).
fof(f215,definition,
( spl16_4
<=> i(triple(sK6,insert_slb(sK5,pair(sK10,sK11)),sK8)) = i(triple(sK7,insert_slb(sK5,pair(sK10,sK11)),sK9)) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f217,plain,
( i(triple(sK6,insert_slb(sK5,pair(sK10,sK11)),sK8)) != i(triple(sK7,insert_slb(sK5,pair(sK10,sK11)),sK9))
| spl16_4 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( ~ spl16_4
| ~ spl16_2
| spl16_3 ),
inference(avatar_split_clause,[],[f197,f211,f207,f215]) ).
fof(f248,plain,
( create_pq != i(triple(sK1,create_slb,sK3))
| spl16_2 ),
inference(forward_demodulation,[],[f209,f194]) ).
fof(f249,plain,
( $false
| spl16_2 ),
inference(forward_subsumption_resolution,[],[f248,f194]) ).
fof(f250,plain,
spl16_2,
inference(avatar_contradiction_clause,[],[f249]) ).
fof(f324,plain,
( ! [X2,X3,X0,X1,X4,X5] : i(insert_cpq(triple(X0,X1,X2),X3)) = i(triple(X4,insert_slb(X1,pair(X3,bottom)),X5))
| ~ spl16_3 ),
inference(superposition,[],[f212,f182]) ).
fof(f465,plain,
( ! [X2,X3,X0,X1,X4,X5] : i(insert_cpq(triple(X0,X1,X2),X3)) = insert_pq(i(triple(X4,X1,X5)),X3)
| ~ spl16_3 ),
inference(forward_demodulation,[],[f324,f195]) ).
fof(f481,plain,
( ! [X0,X1] : i(insert_cpq(triple(sK12,sK13,sK14),sK15)) != i(insert_cpq(triple(X0,sK13,X1),sK15))
| ~ spl16_3 ),
inference(superposition,[],[f198,f465]) ).
fof(f498,plain,
( $false
| ~ spl16_3 ),
inference(equality_resolution,[],[f481]) ).
fof(f499,plain,
~ spl16_3,
inference(avatar_contradiction_clause,[],[f498]) ).
fof(f500,plain,
( i(triple(sK6,insert_slb(sK5,pair(sK10,sK11)),sK8)) != insert_pq(i(triple(sK7,sK5,sK9)),sK10)
| spl16_4 ),
inference(forward_demodulation,[],[f217,f195]) ).
fof(f501,plain,
( insert_pq(i(triple(sK7,sK5,sK9)),sK10) != insert_pq(i(triple(sK6,sK5,sK8)),sK10)
| spl16_4 ),
inference(forward_demodulation,[],[f500,f195]) ).
fof(f527,plain,
( ! [X0,X1] : insert_pq(i(triple(sK6,sK5,sK8)),sK10) != insert_pq(i(triple(X0,sK5,X1)),sK10)
| ~ spl16_1
| spl16_4 ),
inference(superposition,[],[f501,f205]) ).
fof(f533,plain,
( $false
| ~ spl16_1
| spl16_4 ),
inference(equality_resolution,[],[f527]) ).
fof(f534,plain,
( ~ spl16_1
| spl16_4 ),
inference(avatar_contradiction_clause,[],[f533]) ).
cnf(s1,plain,
( spl16_1
| ~ spl16_2
| spl16_3 ),
inference(sat_conversion,[],[f213]) ).
cnf(s2,plain,
( ~ spl16_2
| spl16_3
| ~ spl16_4 ),
inference(sat_conversion,[],[f218]) ).
cnf(s3,plain,
spl16_2,
inference(sat_conversion,[],[f250]) ).
cnf(s4,plain,
~ spl16_3,
inference(sat_conversion,[],[f499]) ).
cnf(s5,plain,
( ~ spl16_1
| spl16_4 ),
inference(sat_conversion,[],[f534]) ).
cnf(s6,plain,
~ spl16_4,
inference(rat,[],[s2,s4,s3]) ).
cnf(s7,plain,
~ spl16_1,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s4,s3,s7]) ).
fof(f535,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV415+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 10:51:34 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.11 Running first-order theorem proving
% 0.08/0.11 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
% 1.72/0.59 % (3308525)Detected formulas, will run a generic FOF schedule.
% 1.72/0.59 % (3308534)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2467047161:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.72/0.59 % (3308532)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=2990066517:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.72/0.59 % (3308533)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3737735054:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.72/0.59 % (3308530)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=920174446:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.72/0.59 % (3308531)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=3728994580:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.72/0.59 % (3308533)Refutation not found, incomplete strategy
% 1.72/0.59 % (3308533)------------------------------
% 1.72/0.59 % (3308533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.72/0.59 % (3308533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.59 % (3308533)CaDiCaL version: 2.1.3
% 1.72/0.59 % (3308533)Termination reason: Refutation not found, incomplete strategy
% 1.72/0.59 % (3308533)Time elapsed: 0.001 s
% 1.72/0.59 % (3308533)Peak memory usage: 88 MB
% 1.72/0.59 % (3308533)Instructions burned: 2 (million)
% 1.72/0.59 % (3308536)dis-21_1_sil=8000:lcm=predicate:random_seed=342573128: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)
% 1.72/0.59 % (3308535)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=185098488:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.72/0.59 % (3308536)Refutation not found, incomplete strategy
% 1.72/0.59 % (3308536)------------------------------
% 1.72/0.59 % (3308536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.72/0.59 % (3308536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.59 % (3308536)CaDiCaL version: 2.1.3
% 1.72/0.59 % (3308536)Termination reason: Refutation not found, incomplete strategy
% 1.72/0.59 % (3308536)Time elapsed: 0.002 s
% 1.72/0.59 % (3308536)Peak memory usage: 88 MB
% 1.72/0.59 % (3308536)Instructions burned: 5 (million)
% 1.72/0.59 % (3308535)First to succeed.
% 1.72/0.59 % (3308535)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3308525"
% 1.72/0.59 % (3308534)Instruction limit reached!
% 1.72/0.59 % (3308534)------------------------------
% 1.72/0.59 % (3308534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.72/0.59 % (3308534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.59 % (3308534)CaDiCaL version: 2.1.3
% 1.72/0.59 % (3308534)Termination reason: Instruction limit
% 1.72/0.59 % (3308534)Termination phase: Saturation
% 1.72/0.59 % (3308534)Time elapsed: 0.029 s
% 1.72/0.59 % (3308534)Peak memory usage: 88 MB
% 1.72/0.59 % (3308534)Instructions burned: 120 (million)
% 1.72/0.59 % (3308544)lrs+10_1_sil=8000:sp=occurrence:random_seed=2223092575:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 1.72/0.59 % (3308544)Also succeeded, but the first one will report.
% 1.72/0.59 % (3308533)------------------------------
% 1.72/0.59 % (3308533)------------------------------
% 1.72/0.59 % (3308536)------------------------------
% 1.72/0.59 % (3308536)------------------------------
% 1.72/0.59 % (3308535)Refutation found. Thanks to Tanya!
% 1.72/0.59 % SZS status Theorem for theBenchmark
% 1.72/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 2.19/0.69 % (3308535)------------------------------
% 2.19/0.69 % (3308535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.19/0.69 % (3308535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.69 % (3308535)CaDiCaL version: 2.1.3
% 2.19/0.69 % (3308535)Termination reason: Refutation
% 2.19/0.69 % (3308535)Time elapsed: 0.010 s
% 2.19/0.69 % (3308535)Peak memory usage: 89 MB
% 2.19/0.69 % (3308535)Instructions burned: 26 (million)
% 2.19/0.69 % (3308535)------------------------------
% 2.19/0.69 % (3308535)------------------------------
% 2.19/0.69 % (3308525)Success in time 0.285 s
% 2.19/0.69 % Vampire exiting
%------------------------------------------------------------------------------