%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CSR077+5 : TPTP v9.3.1. Bugfixed v7.3.0.
% 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 09:42:41 AM UTC 2026
% Result : Theorem 0.08s 1.03s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 14 unt; 2 def)
% Number of atoms : 124 ( 41 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 130 ( 48 ~; 52 |; 22 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4433,axiom,
! [X0,X1] :
( ( s__AbsoluteValueFn(X1) = X0
& s__instance(X1,s__RealNumber)
& s__instance(X0,s__RealNumber) )
<=> ( ( s__instance(X1,s__NonnegativeRealNumber)
& X1 = X0 )
| ( s__instance(X1,s__NegativeRealNumber)
& X0 = minus("0",X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kb_SUMO_4445) ).
fof(f4596,axiom,
! [X0] :
( s__instance(X0,s__RealNumber)
=> ( s__instance(X0,s__NonnegativeRealNumber)
=> ( s__SignumFn(X0) = "1"
| s__SignumFn(X0) = "0" ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kb_SUMO_4608) ).
fof(f4598,axiom,
! [X0] :
( s__instance(X0,s__RealNumber)
=> ( s__instance(X0,s__NegativeRealNumber)
=> s__SignumFn(X0) = "-1" ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kb_SUMO_4610) ).
fof(f16749,axiom,
s__instance(s__Number3_1,s__NonnegativeRealNumber),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',local_1) ).
fof(f16750,conjecture,
~ s__instance(s__Number3_1,s__NegativeRealNumber),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_from_SUMO_MILO) ).
fof(f16751,negated_conjecture,
~ ~ s__instance(s__Number3_1,s__NegativeRealNumber),
inference(negated_conjecture,[status(cth)],[f16750]) ).
fof(f16752,plain,
s__instance(s__Number3_1,s__NegativeRealNumber),
inference(flattening,[],[f16751]) ).
fof(f16762,plain,
! [X0] :
( s__SignumFn(X0) = "-1"
| ~ s__instance(X0,s__NegativeRealNumber)
| ~ s__instance(X0,s__RealNumber) ),
inference(ennf_transformation,[],[f4598]) ).
fof(f16763,plain,
! [X0] :
( s__SignumFn(X0) = "-1"
| ~ s__instance(X0,s__NegativeRealNumber)
| ~ s__instance(X0,s__RealNumber) ),
inference(flattening,[],[f16762]) ).
fof(f16780,plain,
! [X0] :
( s__SignumFn(X0) = "1"
| s__SignumFn(X0) = "0"
| ~ s__instance(X0,s__NonnegativeRealNumber)
| ~ s__instance(X0,s__RealNumber) ),
inference(ennf_transformation,[],[f4596]) ).
fof(f16781,plain,
! [X0] :
( s__SignumFn(X0) = "1"
| s__SignumFn(X0) = "0"
| ~ s__instance(X0,s__NonnegativeRealNumber)
| ~ s__instance(X0,s__RealNumber) ),
inference(flattening,[],[f16780]) ).
fof(f16885,definition,
! [X0,X1] :
( sP0(X0,X1)
<=> ( s__AbsoluteValueFn(X1) = X0
& s__instance(X1,s__RealNumber)
& s__instance(X0,s__RealNumber) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f16886,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ( s__instance(X1,s__NonnegativeRealNumber)
& X1 = X0 )
| ( s__instance(X1,s__NegativeRealNumber)
& X0 = minus("0",X1) ) ) ),
inference(definition_folding,[],[f4433,f16885]) ).
fof(f16887,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| s__AbsoluteValueFn(X1) != X0
| ~ s__instance(X1,s__RealNumber)
| ~ s__instance(X0,s__RealNumber) )
& ( ( s__AbsoluteValueFn(X1) = X0
& s__instance(X1,s__RealNumber)
& s__instance(X0,s__RealNumber) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f16885]) ).
fof(f16888,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| s__AbsoluteValueFn(X1) != X0
| ~ s__instance(X1,s__RealNumber)
| ~ s__instance(X0,s__RealNumber) )
& ( ( s__AbsoluteValueFn(X1) = X0
& s__instance(X1,s__RealNumber)
& s__instance(X0,s__RealNumber) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f16887]) ).
fof(f16889,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ s__instance(X1,s__NonnegativeRealNumber)
| X0 != X1 )
& ( ~ s__instance(X1,s__NegativeRealNumber)
| minus("0",X1) != X0 ) ) )
& ( ( s__instance(X1,s__NonnegativeRealNumber)
& X1 = X0 )
| ( s__instance(X1,s__NegativeRealNumber)
& X0 = minus("0",X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f16886]) ).
fof(f16890,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ s__instance(X1,s__NonnegativeRealNumber)
| X0 != X1 )
& ( ~ s__instance(X1,s__NegativeRealNumber)
| minus("0",X1) != X0 ) ) )
& ( ( s__instance(X1,s__NonnegativeRealNumber)
& X1 = X0 )
| ( s__instance(X1,s__NegativeRealNumber)
& X0 = minus("0",X1) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f16889]) ).
fof(f16907,plain,
s__instance(s__Number3_1,s__NegativeRealNumber),
inference(cnf_transformation,[],[f16752]) ).
fof(f16908,plain,
! [X0] :
( ~ s__instance(X0,s__NegativeRealNumber)
| "-1" = s__SignumFn(X0)
| ~ s__instance(X0,s__RealNumber) ),
inference(cnf_transformation,[],[f16763]) ).
fof(f16909,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| s__instance(X0,s__RealNumber) ),
inference(cnf_transformation,[],[f16888]) ).
fof(f16918,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ s__instance(X1,s__NonnegativeRealNumber)
| X0 != X1 ),
inference(cnf_transformation,[],[f16890]) ).
fof(f16925,plain,
s__instance(s__Number3_1,s__NonnegativeRealNumber),
inference(cnf_transformation,[],[f16749]) ).
fof(f16945,plain,
! [X0] :
( ~ s__instance(X0,s__NonnegativeRealNumber)
| "0" = s__SignumFn(X0)
| "1" = s__SignumFn(X0)
| ~ s__instance(X0,s__RealNumber) ),
inference(cnf_transformation,[],[f16781]) ).
fof(f17039,plain,
! [X1] :
( ~ s__instance(X1,s__NonnegativeRealNumber)
| sP0(X1,X1) ),
inference(equality_resolution,[],[f16918]) ).
fof(f17118,plain,
sP0(s__Number3_1,s__Number3_1),
inference(resolution,[],[f17039,f16925]) ).
fof(f17148,definition,
( spl6_2
<=> s__instance(s__Number3_1,s__RealNumber) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f17150,plain,
( s__instance(s__Number3_1,s__RealNumber)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f17148]) ).
fof(f17164,plain,
s__instance(s__Number3_1,s__RealNumber),
inference(resolution,[],[f17118,f16909]) ).
fof(f17165,plain,
spl6_2,
inference(avatar_split_clause,[],[f17164,f17148]) ).
fof(f17443,plain,
( "-1" = s__SignumFn(s__Number3_1)
| ~ s__instance(s__Number3_1,s__RealNumber) ),
inference(resolution,[],[f16908,f16907]) ).
fof(f17444,plain,
( "-1" = s__SignumFn(s__Number3_1)
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f17443,f17150]) ).
fof(f17480,plain,
( "0" = s__SignumFn(s__Number3_1)
| "1" = s__SignumFn(s__Number3_1)
| ~ s__instance(s__Number3_1,s__RealNumber) ),
inference(resolution,[],[f16945,f16925]) ).
fof(f17481,plain,
( "0" = s__SignumFn(s__Number3_1)
| "1" = s__SignumFn(s__Number3_1)
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f17480,f17150]) ).
fof(f17482,plain,
( "-1" = "0"
| "1" = s__SignumFn(s__Number3_1)
| ~ spl6_2 ),
inference(forward_demodulation,[],[f17481,f17444]) ).
fof(f17483,plain,
( "1" = s__SignumFn(s__Number3_1)
| ~ spl6_2 ),
inference(distinct_equality_removal,[],[f17482]) ).
fof(f17484,plain,
( "1" = "-1"
| ~ spl6_2 ),
inference(superposition,[],[f17483,f17444]) ).
fof(f17488,plain,
( $false
| ~ spl6_2 ),
inference(distinct_equality_removal,[],[f17484]) ).
fof(f17489,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f17488]) ).
cnf(s2,plain,
spl6_2,
inference(sat_conversion,[],[f17165]) ).
cnf(s24,plain,
~ spl6_2,
inference(sat_conversion,[],[f17489]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s2,s24]) ).
fof(f17490,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CSR077+5 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Mon Sep 28 22:27:04 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running first-order theorem proving
% 0.06/0.13 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
% 2.44/0.92 % (3866490)Detected formulas, will run a generic FOF schedule.
% 2.44/0.92 % (3866496)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=1598566676:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 2.44/0.92 % (3866497)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=826040386:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 2.44/0.92 % (3866495)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=1245457529:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 2.44/0.92 % (3866498)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1260412956:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 2.44/0.92 % (3866501)dis-21_1_sil=8000:lcm=predicate:random_seed=3130062720:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 2.44/0.92 % (3866499)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1387247491:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 2.44/0.92 % (3866500)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3897698555:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 2.44/0.92 % (3866498)Refutation not found, incomplete strategy
% 2.44/0.92 % (3866498)------------------------------
% 2.44/0.92 % (3866498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/0.92 % (3866498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.92 % (3866498)CaDiCaL version: 2.1.3
% 2.44/0.92 % (3866498)Termination reason: Refutation not found, incomplete strategy
% 2.44/0.92 % (3866498)Time elapsed: 0.021 s
% 2.44/0.92 % (3866498)Peak memory usage: 102 MB
% 2.44/0.92 % (3866498)Instructions burned: 59 (million)
% 2.44/0.92 % (3866501)Instruction limit reached!
% 2.44/0.92 % (3866501)------------------------------
% 2.44/0.92 % (3866501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/0.92 % (3866501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.92 % (3866501)CaDiCaL version: 2.1.3
% 2.44/0.92 % (3866501)Termination reason: Instruction limit
% 2.44/0.92 % (3866501)Termination phase: Saturation
% 2.44/0.92 % (3866501)Time elapsed: 0.045 s
% 2.44/0.92 % (3866501)Peak memory usage: 103 MB
% 2.44/0.92 % (3866501)Instructions burned: 132 (million)
% 2.44/0.92 % (3866500)Instruction limit reached!
% 2.44/0.92 % (3866500)------------------------------
% 2.44/0.92 % (3866500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/0.92 % (3866500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.92 % (3866500)CaDiCaL version: 2.1.3
% 2.44/0.92 % (3866500)Termination reason: Instruction limit
% 2.44/0.92 % (3866500)Termination phase: SInE selection
% 2.44/0.92 % (3866500)Time elapsed: 0.042 s
% 2.44/0.92 % (3866500)Peak memory usage: 99 MB
% 2.44/0.92 % (3866500)Instructions burned: 139 (million)
% 2.44/0.92 % (3866499)Instruction limit reached!
% 2.44/0.92 % (3866499)------------------------------
% 2.44/0.92 % (3866499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/0.92 % (3866499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.92 % (3866499)CaDiCaL version: 2.1.3
% 2.44/0.92 % (3866499)Termination reason: Instruction limit
% 2.44/0.92 % (3866499)Termination phase: Saturation
% 2.44/0.92 % (3866499)Time elapsed: 0.044 s
% 2.44/0.92 % (3866499)Peak memory usage: 102 MB
% 2.44/0.92 % (3866499)Instructions burned: 123 (million)
% 2.44/0.92 % (3866509)lrs+10_1_sil=8000:sp=occurrence:random_seed=1896668521:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 2.44/0.92 % (3866510)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3793709059:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 2.44/0.92 % (3866511)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3807881791:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 2.44/0.92 % (3866509)First to succeed.
% 2.44/0.92 % (3866509)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3866490"
% 2.44/0.92 % (3866498)------------------------------
% 2.44/0.92 % (3866498)------------------------------
% 2.44/0.92 % (3866510)Refutation not found, incomplete strategy
% 0.08/1.03 % (3866510)------------------------------
% 0.08/1.03 % (3866510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.03 % (3866510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.03 % (3866510)CaDiCaL version: 2.1.3
% 0.08/1.03 % (3866510)Termination reason: Refutation not found, incomplete strategy
% 0.08/1.03 % (3866510)Time elapsed: 0.049 s
% 0.08/1.03 % (3866510)Peak memory usage: 103 MB
% 0.08/1.03 % (3866510)Instructions burned: 156 (million)
% 0.08/1.03 % (3866511)Instruction limit reached!
% 0.08/1.03 % (3866511)------------------------------
% 0.08/1.03 % (3866511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.03 % (3866511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.03 % (3866511)CaDiCaL version: 2.1.3
% 0.08/1.03 % (3866511)Termination reason: Instruction limit
% 0.08/1.03 % (3866511)Termination phase: Saturation
% 0.08/1.03 % (3866511)Time elapsed: 0.092 s
% 0.08/1.03 % (3866511)Peak memory usage: 103 MB
% 0.08/1.03 % (3866511)Instructions burned: 327 (million)
% 0.08/1.03 % (3866515)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=371853490:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 0.08/1.03 % (3866509)Refutation found. Thanks to Tanya!
% 0.08/1.03 % SZS status Theorem for theBenchmark
% 0.08/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/1.03 % (3866509)------------------------------
% 0.08/1.03 % (3866509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.03 % (3866509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.03 % (3866509)CaDiCaL version: 2.1.3
% 0.08/1.03 % (3866509)Termination reason: Refutation
% 0.08/1.03 % (3866509)Time elapsed: 0.030 s
% 0.08/1.03 % (3866509)Peak memory usage: 104 MB
% 0.08/1.03 % (3866509)Instructions burned: 67 (million)
% 0.08/1.03 % (3866509)------------------------------
% 0.08/1.03 % (3866509)------------------------------
% 0.08/1.03 % (3866490)Success in time 0.599 s
% 0.08/1.03 % Vampire exiting
%------------------------------------------------------------------------------