%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM651_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:16:12 PM UTC 2026
% Result : Theorem 2.48s 1.08s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 148 ( 84 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 100 ~; 52 |; 12 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 34 !; 12 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
y: nat ).
tff(func_def_2,type,
pl: ( nat * nat ) > nat ).
tff(func_def_5,type,
sK0: nat ).
tff(func_def_6,type,
sK1: nat ).
tff(func_def_7,type,
sK2: nat ).
tff(func_def_8,type,
sK3: nat ).
tff(f1,axiom,
! [X0: nat,X1: nat] : ( X1 != pl(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz7) ).
tff(f2,axiom,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] : ( pl(pl(X0,X1),X2) = pl(X0,pl(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
tff(f5,conjecture,
~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] : ( x != pl(y,X0) ) )
=> ~ ~ ( ( ~ ! [X0: nat] : ( x != pl(y,X0) )
=> ~ ~ ! [X0: nat] : ( y != pl(x,X0) ) )
=> ~ ( ~ ! [X0: nat] : ( y != pl(x,X0) )
=> ( x != y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz9b) ).
tff(f6,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] : ( x != pl(y,X0) ) )
=> ~ ~ ( ( ~ ! [X0: nat] : ( x != pl(y,X0) )
=> ~ ~ ! [X0: nat] : ( y != pl(x,X0) ) )
=> ~ ( ~ ! [X0: nat] : ( y != pl(x,X0) )
=> ( x != y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f10,plain,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] : ( x != pl(y,X0) ) )
=> ~ ~ ( ( ~ ! [X1: nat] : ( x != pl(y,X1) )
=> ~ ~ ! [X2: nat] : ( y != pl(x,X2) ) )
=> ~ ( ~ ! [X3: nat] : ( y != pl(x,X3) )
=> ( x != y ) ) ) ),
inference(rectify,[],[f6]) ).
tff(f11,plain,
( ( ( x = y )
=> ! [X0: nat] : ( x != pl(y,X0) ) )
=> ( ( ~ ! [X1: nat] : ( x != pl(y,X1) )
=> ! [X2: nat] : ( y != pl(x,X2) ) )
=> ~ ( ~ ! [X3: nat] : ( y != pl(x,X3) )
=> ( x != y ) ) ) ),
inference(flattening,[],[f10]) ).
tff(f13,plain,
( ( ( x = y )
& ? [X3: nat] : ( y = pl(x,X3) ) )
| ( ? [X2: nat] : ( y = pl(x,X2) )
& ? [X1: nat] : ( x = pl(y,X1) ) )
| ( ? [X0: nat] : ( x = pl(y,X0) )
& ( x = y ) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f14,plain,
( ( ( x = y )
& ? [X3: nat] : ( y = pl(x,X3) ) )
| ( ? [X2: nat] : ( y = pl(x,X2) )
& ? [X1: nat] : ( x = pl(y,X1) ) )
| ( ? [X0: nat] : ( x = pl(y,X0) )
& ( x = y ) ) ),
inference(flattening,[],[f13]) ).
tff(f15,plain,
( ( ( x = y )
& ? [X0: nat] : ( y = pl(x,X0) ) )
| ( ? [X1: nat] : ( y = pl(x,X1) )
& ? [X2: nat] : ( x = pl(y,X2) ) )
| ( ? [X3: nat] : ( x = pl(y,X3) )
& ( x = y ) ) ),
inference(rectify,[],[f14]) ).
tff(f16,plain,
( ( ( x = y )
& ( y = pl(x,sK0) ) )
| ( ( y = pl(x,sK1) )
& ( x = pl(y,sK2) ) )
| ( ( x = pl(y,sK3) )
& ( x = y ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
tff(f17,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) != X1 ),
inference(cnf_transformation,[],[f1]) ).
tff(f18,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
inference(cnf_transformation,[],[f2]) ).
tff(f20,plain,
! [X2: nat,X0: nat,X1: nat] : ( pl(pl(X0,X1),X2) = pl(X0,pl(X1,X2)) ),
inference(cnf_transformation,[],[f4]) ).
tff(f24,plain,
( ( y = pl(x,sK0) )
| ( y = pl(x,sK1) )
| ( x = pl(y,sK3) ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f25,plain,
( ( x = y )
| ( x = pl(y,sK2) )
| ( x = y ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f27,plain,
( ( x = y )
| ( y = pl(x,sK1) )
| ( x = y ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f32,plain,
( ( x = y )
| ( x = pl(y,sK2) ) ),
inference(duplicate_literal_removal,[],[f25]) ).
tff(f33,plain,
( ( x = y )
| ( y = pl(x,sK1) ) ),
inference(duplicate_literal_removal,[],[f27]) ).
tff(f35,definition,
( spl4_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f37,plain,
( ( x = y )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f39,definition,
( spl4_2
<=> ( x = pl(y,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f41,plain,
( ( x = pl(y,sK2) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f43,definition,
( spl4_3
<=> ( y = pl(x,sK0) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f45,plain,
( ( y = pl(x,sK0) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f43]) ).
tff(f48,definition,
( spl4_4
<=> ( x = pl(y,sK3) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f50,plain,
( ( x = pl(y,sK3) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f53,definition,
( spl4_5
<=> ( y = pl(x,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f55,plain,
( ( y = pl(x,sK1) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f53]) ).
tff(f57,plain,
( spl4_4
| spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f24,f43,f53,f48]) ).
tff(f58,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f32,f35,f39]) ).
tff(f60,plain,
( spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f33,f35,f53]) ).
tff(f64,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) != X0 ),
inference(superposition,[],[f17,f18]) ).
tff(f68,plain,
( ! [X0: nat] : ( pl(y,X0) = pl(x,pl(sK1,X0)) )
| ~ spl4_5 ),
inference(superposition,[],[f20,f55]) ).
tff(f94,plain,
( ( x != y )
| ~ spl4_5 ),
inference(superposition,[],[f64,f55]) ).
tff(f95,plain,
( ! [X0: nat] : ( x != pl(y,X0) )
| ~ spl4_5 ),
inference(superposition,[],[f64,f68]) ).
tff(f100,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f94,f53,f35]) ).
tff(f101,plain,
( ( x != x )
| ~ spl4_2
| ~ spl4_5 ),
inference(superposition,[],[f95,f41]) ).
tff(f105,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f101]) ).
tff(f106,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f105]) ).
tff(f108,plain,
( ( x = pl(x,sK0) )
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f45,f37]) ).
tff(f109,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f108,f64]) ).
tff(f110,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f109]) ).
tff(f112,plain,
( ( x = pl(x,sK3) )
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_demodulation,[],[f50,f37]) ).
tff(f113,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f112,f64]) ).
tff(f114,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f113]) ).
cnf(s4,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f57]) ).
cnf(s5,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f58]) ).
cnf(s7,plain,
( spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f60]) ).
cnf(s10,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f100]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f106]) ).
cnf(s12,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f110]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f114]) ).
cnf(s14,plain,
spl4_1,
inference(rat,[],[s11,s5,s7]) ).
cnf(s15,plain,
~ spl4_4,
inference(rat,[],[s13,s14]) ).
cnf(s16,plain,
~ spl4_3,
inference(rat,[],[s12,s14]) ).
cnf(s17,plain,
~ spl4_5,
inference(rat,[],[s10,s14]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s4,s17,s15,s16]) ).
tff(f115,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM651_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 21:01:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.48/1.08 % (2983276)Detected formulas, will run a generic FOF schedule.
% 2.48/1.08 % (2983286)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1547432370:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.48/1.08 % (2983286)First to succeed.
% 2.48/1.08 % (2983286)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2983276"
% 2.48/1.08 % (2983284)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2578676615:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.48/1.08 % (2983285)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3247501631:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.48/1.08 % (2983281)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=1826478585:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.48/1.08 % (2983283)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=2795669499:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.48/1.08 % (2983282)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=2231156479:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.48/1.08 % (2983287)dis-21_1_sil=8000:lcm=predicate:random_seed=3287700752: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)
% 2.48/1.08 % (2983287)Refutation not found, incomplete strategy
% 2.48/1.08 % (2983287)------------------------------
% 2.48/1.08 % (2983287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.08 % (2983287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.08 % (2983287)CaDiCaL version: 2.1.3
% 2.48/1.08 % (2983287)Termination reason: Refutation not found, incomplete strategy
% 2.48/1.08 % (2983287)Time elapsed: 0.002 s
% 2.48/1.08 % (2983287)Peak memory usage: 88 MB
% 2.48/1.08 % (2983287)Instructions burned: 1 (million)
% 2.48/1.08 % (2983285)Also succeeded, but the first one will report.
% 2.48/1.08 % (2983284)Instruction limit reached!
% 2.48/1.08 % (2983284)------------------------------
% 2.48/1.08 % (2983284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.08 % (2983284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.08 % (2983284)CaDiCaL version: 2.1.3
% 2.48/1.08 % (2983284)Termination reason: Instruction limit
% 2.48/1.08 % (2983284)Termination phase: Saturation
% 2.48/1.08 % (2983284)Time elapsed: 0.063 s
% 2.48/1.08 % (2983284)Peak memory usage: 89 MB
% 2.48/1.08 % (2983284)Instructions burned: 109 (million)
% 2.48/1.08 % (2983286)Refutation found. Thanks to Tanya!
% 2.48/1.08 % SZS status Theorem for theBenchmark
% 2.48/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 2.48/1.09 % (2983286)------------------------------
% 2.48/1.09 % (2983286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.09 % (2983286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.09 % (2983286)CaDiCaL version: 2.1.3
% 2.48/1.09 % (2983286)Termination reason: Refutation
% 2.48/1.09 % (2983286)Time elapsed: 0.003 s
% 2.48/1.09 % (2983286)Peak memory usage: 90 MB
% 2.48/1.09 % (2983286)Instructions burned: 5 (million)
% 2.48/1.09 % (2983286)------------------------------
% 2.48/1.09 % (2983286)------------------------------
% 2.48/1.09 % (2983276)Success in time 0.299 s
% 2.48/1.09 % Vampire exiting
%------------------------------------------------------------------------------