%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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 02:00:56 PM UTC 2026
% Result : Theorem 0.63s 0.93s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of formulae : 78 ( 8 unt; 1 def)
% Number of atoms : 303 ( 212 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 361 ( 136 ~; 162 |; 50 &)
% ( 4 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 94 ( 64 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ? [X0] : X0 = f(g(X0))
& ! [X1,X2] :
( ( X1 = f(g(X1))
& X2 = f(g(X2)) )
=> X1 = X2 ) )
<=> ( ? [X0] : X0 = g(f(X0))
& ! [X1,X2] :
( ( X1 = g(f(X1))
& X2 = g(f(X2)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_cute_thing) ).
fof(f2,negated_conjecture,
~ ( ( ? [X0] : X0 = f(g(X0))
& ! [X1,X2] :
( ( X1 = f(g(X1))
& X2 = f(g(X2)) )
=> X1 = X2 ) )
<=> ( ? [X0] : X0 = g(f(X0))
& ! [X1,X2] :
( ( X1 = g(f(X1))
& X2 = g(f(X2)) )
=> X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ? [X0] : X0 = f(g(X0))
& ! [X1,X2] :
( ( X1 = f(g(X1))
& X2 = f(g(X2)) )
=> X1 = X2 ) )
<=> ( ? [X3] : g(f(X3)) = X3
& ! [X4,X5] :
( ( g(f(X4)) = X4
& g(f(X5)) = X5 )
=> X4 = X5 ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ( ? [X0] : X0 = f(g(X0))
& ! [X1,X2] :
( X1 = X2
| f(g(X1)) != X1
| f(g(X2)) != X2 ) )
<~> ( ? [X3] : g(f(X3)) = X3
& ! [X4,X5] :
( X4 = X5
| g(f(X4)) != X4
| g(f(X5)) != X5 ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ? [X0] : X0 = f(g(X0))
& ! [X1,X2] :
( X1 = X2
| f(g(X1)) != X1
| f(g(X2)) != X2 ) )
<~> ( ? [X3] : g(f(X3)) = X3
& ! [X4,X5] :
( X4 = X5
| g(f(X4)) != X4
| g(f(X5)) != X5 ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,definition,
( sP0
<=> ( ? [X0] : X0 = f(g(X0))
& ! [X1,X2] :
( X1 = X2
| f(g(X1)) != X1
| f(g(X2)) != X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f7,plain,
( sP0
<~> ( ? [X3] : g(f(X3)) = X3
& ! [X4,X5] :
( X4 = X5
| g(f(X4)) != X4
| g(f(X5)) != X5 ) ) ),
inference(definition_folding,[],[f5,f6]) ).
fof(f8,plain,
( ( sP0
| ! [X0] : f(g(X0)) != X0
| ? [X1,X2] :
( X1 != X2
& f(g(X1)) = X1
& f(g(X2)) = X2 ) )
& ( ( ? [X0] : X0 = f(g(X0))
& ! [X1,X2] :
( X1 = X2
| f(g(X1)) != X1
| f(g(X2)) != X2 ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( sP0
| ! [X0] : f(g(X0)) != X0
| ? [X1,X2] :
( X1 != X2
& f(g(X1)) = X1
& f(g(X2)) = X2 ) )
& ( ( ? [X0] : X0 = f(g(X0))
& ! [X1,X2] :
( X1 = X2
| f(g(X1)) != X1
| f(g(X2)) != X2 ) )
| ~ sP0 ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
( ( sP0
| ! [X0] : f(g(X0)) != X0
| ? [X1,X2] :
( X1 != X2
& f(g(X1)) = X1
& f(g(X2)) = X2 ) )
& ( ( ? [X3] : f(g(X3)) = X3
& ! [X4,X5] :
( X4 = X5
| f(g(X4)) != X4
| f(g(X5)) != X5 ) )
| ~ sP0 ) ),
inference(rectify,[],[f9]) ).
fof(f11,plain,
( ( sP0
| ! [X0] : f(g(X0)) != X0
| ( sK1 != sK2
& sK1 = f(g(sK1))
& sK2 = f(g(sK2)) ) )
& ( ( sK3 = f(g(sK3))
& ! [X4,X5] :
( X4 = X5
| f(g(X4)) != X4
| f(g(X5)) != X5 ) )
| ~ sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f10]) ).
fof(f12,plain,
( ( ! [X3] : g(f(X3)) != X3
| ? [X4,X5] :
( X4 != X5
& g(f(X4)) = X4
& g(f(X5)) = X5 )
| ~ sP0 )
& ( ( ? [X3] : g(f(X3)) = X3
& ! [X4,X5] :
( X4 = X5
| g(f(X4)) != X4
| g(f(X5)) != X5 ) )
| sP0 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f13,plain,
( ( ! [X3] : g(f(X3)) != X3
| ? [X4,X5] :
( X4 != X5
& g(f(X4)) = X4
& g(f(X5)) = X5 )
| ~ sP0 )
& ( ( ? [X3] : g(f(X3)) = X3
& ! [X4,X5] :
( X4 = X5
| g(f(X4)) != X4
| g(f(X5)) != X5 ) )
| sP0 ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ( ! [X0] : g(f(X0)) != X0
| ? [X1,X2] :
( X1 != X2
& g(f(X1)) = X1
& g(f(X2)) = X2 )
| ~ sP0 )
& ( ( ? [X3] : g(f(X3)) = X3
& ! [X4,X5] :
( X4 = X5
| g(f(X4)) != X4
| g(f(X5)) != X5 ) )
| sP0 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
( ( ! [X0] : g(f(X0)) != X0
| ( sK4 != sK5
& sK4 = g(f(sK4))
& sK5 = g(f(sK5)) )
| ~ sP0 )
& ( ( sK6 = g(f(sK6))
& ! [X4,X5] :
( X4 = X5
| g(f(X4)) != X4
| g(f(X5)) != X5 ) )
| sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f14]) ).
fof(f16,plain,
! [X4,X5] :
( f(g(X5)) != X5
| f(g(X4)) != X4
| X4 = X5
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
( sK3 = f(g(sK3))
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0] :
( f(g(X0)) != X0
| sP0
| sK2 = f(g(sK2)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
! [X0] :
( f(g(X0)) != X0
| sP0
| sK1 = f(g(sK1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X0] :
( f(g(X0)) != X0
| sP0
| sK1 != sK2 ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X4,X5] :
( g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5
| sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
( sK6 = g(f(sK6))
| sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0] :
( g(f(X0)) != X0
| sK5 = g(f(sK5))
| ~ sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0] :
( g(f(X0)) != X0
| sK4 = g(f(sK4))
| ~ sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0] :
( g(f(X0)) != X0
| sK4 != sK5
| ~ sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0] :
( sK6 != sK6
| g(f(X0)) != X0
| sK6 = X0
| sP0
| sP0 ),
inference(superposition,[],[f21,f22]) ).
fof(f30,plain,
! [X0] :
( sK6 != sK6
| g(f(X0)) != X0
| sK6 = X0
| sP0 ),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f31,plain,
! [X0] :
( g(f(X0)) != X0
| sK6 = X0
| sP0 ),
inference(trivial_inequality_removal,[],[f30]) ).
fof(f34,plain,
( g(sK3) != g(sK3)
| sK4 = g(f(sK4))
| ~ sP0
| ~ sP0 ),
inference(superposition,[],[f24,f17]) ).
fof(f35,plain,
( g(sK3) != g(sK3)
| sK5 = g(f(sK5))
| ~ sP0
| ~ sP0 ),
inference(superposition,[],[f23,f17]) ).
fof(f36,plain,
( g(sK3) != g(sK3)
| sK4 != sK5
| ~ sP0
| ~ sP0 ),
inference(superposition,[],[f25,f17]) ).
fof(f37,plain,
( g(sK3) != g(sK3)
| sK4 != sK5
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f38,plain,
( sK4 != sK5
| ~ sP0 ),
inference(trivial_inequality_removal,[],[f37]) ).
fof(f39,plain,
( g(sK3) != g(sK3)
| sK5 = g(f(sK5))
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f35]) ).
fof(f40,plain,
( sK5 = g(f(sK5))
| ~ sP0 ),
inference(trivial_inequality_removal,[],[f39]) ).
fof(f41,plain,
( g(sK3) != g(sK3)
| sK4 = g(f(sK4))
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f34]) ).
fof(f42,plain,
( sK4 = g(f(sK4))
| ~ sP0 ),
inference(trivial_inequality_removal,[],[f41]) ).
fof(f43,plain,
( f(sK6) != f(sK6)
| sP0
| sK1 != sK2
| sP0 ),
inference(superposition,[],[f20,f22]) ).
fof(f45,plain,
( f(sK6) != f(sK6)
| sP0
| sK1 != sK2 ),
inference(duplicate_literal_removal,[],[f43]) ).
fof(f46,plain,
( sK1 != sK2
| sP0 ),
inference(trivial_inequality_removal,[],[f45]) ).
fof(f56,plain,
( f(sK6) != f(sK6)
| sP0
| sK2 = f(g(sK2))
| sP0 ),
inference(superposition,[],[f18,f22]) ).
fof(f59,plain,
( f(sK6) != f(sK6)
| sP0
| sK2 = f(g(sK2)) ),
inference(duplicate_literal_removal,[],[f56]) ).
fof(f60,plain,
( sK2 = f(g(sK2))
| sP0 ),
inference(trivial_inequality_removal,[],[f59]) ).
fof(f71,plain,
( f(sK6) != f(sK6)
| sP0
| sK1 = f(g(sK1))
| sP0 ),
inference(superposition,[],[f19,f22]) ).
fof(f75,plain,
( f(sK6) != f(sK6)
| sP0
| sK1 = f(g(sK1)) ),
inference(duplicate_literal_removal,[],[f71]) ).
fof(f76,plain,
( sK1 = f(g(sK1))
| sP0 ),
inference(trivial_inequality_removal,[],[f75]) ).
fof(f79,plain,
( g(sK2) != g(sK2)
| g(sK2) = sK6
| sP0
| sP0 ),
inference(superposition,[],[f31,f60]) ).
fof(f86,plain,
( g(sK2) != g(sK2)
| g(sK2) = sK6
| sP0 ),
inference(duplicate_literal_removal,[],[f79]) ).
fof(f87,plain,
( g(sK2) = sK6
| sP0 ),
inference(trivial_inequality_removal,[],[f86]) ).
fof(f92,plain,
( sK2 = f(sK6)
| sP0
| sP0 ),
inference(superposition,[],[f60,f87]) ).
fof(f99,plain,
( sK2 = f(sK6)
| sP0 ),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f104,plain,
! [X0] :
( sK3 != sK3
| f(g(X0)) != X0
| sK3 = X0
| ~ sP0
| ~ sP0 ),
inference(superposition,[],[f16,f17]) ).
fof(f106,plain,
! [X0] :
( sK3 != sK3
| f(g(X0)) != X0
| sK3 = X0
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f107,plain,
! [X0] :
( f(g(X0)) != X0
| sK3 = X0
| ~ sP0 ),
inference(trivial_inequality_removal,[],[f106]) ).
fof(f122,plain,
( g(sK1) != g(sK1)
| g(sK1) = sK6
| sP0
| sP0 ),
inference(superposition,[],[f31,f76]) ).
fof(f129,plain,
( g(sK1) != g(sK1)
| g(sK1) = sK6
| sP0 ),
inference(duplicate_literal_removal,[],[f122]) ).
fof(f130,plain,
( g(sK1) = sK6
| sP0 ),
inference(trivial_inequality_removal,[],[f129]) ).
fof(f135,plain,
( sK1 = f(sK6)
| sP0
| sP0 ),
inference(superposition,[],[f76,f130]) ).
fof(f143,plain,
( sK1 = f(sK6)
| sP0 ),
inference(duplicate_literal_removal,[],[f135]) ).
fof(f145,plain,
( sK1 = sK2
| sP0
| sP0 ),
inference(superposition,[],[f99,f143]) ).
fof(f153,plain,
( sK1 = sK2
| sP0 ),
inference(duplicate_literal_removal,[],[f145]) ).
fof(f155,plain,
sP0,
inference(forward_subsumption_resolution,[],[f153,f46]) ).
fof(f158,plain,
( f(sK5) != f(sK5)
| sK3 = f(sK5)
| ~ sP0
| ~ sP0 ),
inference(superposition,[],[f107,f40]) ).
fof(f159,plain,
( f(sK4) != f(sK4)
| sK3 = f(sK4)
| ~ sP0
| ~ sP0 ),
inference(superposition,[],[f107,f42]) ).
fof(f164,plain,
( f(sK4) != f(sK4)
| sK3 = f(sK4)
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f159]) ).
fof(f165,plain,
( sK3 = f(sK4)
| ~ sP0 ),
inference(trivial_inequality_removal,[],[f164]) ).
fof(f166,plain,
( f(sK5) != f(sK5)
| sK3 = f(sK5)
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f158]) ).
fof(f167,plain,
( sK3 = f(sK5)
| ~ sP0 ),
inference(trivial_inequality_removal,[],[f166]) ).
fof(f168,plain,
sK3 = f(sK4),
inference(forward_subsumption_resolution,[],[f165,f155]) ).
fof(f169,plain,
( g(sK3) = sK4
| ~ sP0 ),
inference(superposition,[],[f42,f168]) ).
fof(f175,plain,
g(sK3) = sK4,
inference(forward_subsumption_resolution,[],[f169,f155]) ).
fof(f176,plain,
sK3 = f(sK5),
inference(forward_subsumption_resolution,[],[f167,f155]) ).
fof(f177,plain,
( g(sK3) = sK5
| ~ sP0 ),
inference(superposition,[],[f40,f176]) ).
fof(f183,plain,
g(sK3) = sK5,
inference(forward_subsumption_resolution,[],[f177,f155]) ).
fof(f189,plain,
sK4 = sK5,
inference(forward_demodulation,[],[f183,f175]) ).
fof(f192,plain,
( sK4 != sK4
| ~ sP0 ),
inference(superposition,[],[f38,f189]) ).
fof(f193,plain,
~ sP0,
inference(trivial_inequality_removal,[],[f192]) ).
fof(f194,plain,
$false,
inference(forward_subsumption_resolution,[],[f193,f155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 16:33:04 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 0.63/0.93 % (3748496)Detected formulas, will run a generic FOF schedule.
% 0.63/0.93 % (3748505)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=469387718:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.63/0.93 % (3748505)First to succeed.
% 0.63/0.93 % (3748505)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3748496"
% 0.63/0.93 % (3748504)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3959997361:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.63/0.93 % (3748503)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=2505857211:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.63/0.93 % (3748502)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=3786754927:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.63/0.93 % (3748501)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=1270505252:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.63/0.93 % (3748504)Also succeeded, but the first one will report.
% 0.63/0.93 % (3748507)dis-21_1_sil=8000:lcm=predicate:random_seed=210132477: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)
% 0.63/0.93 % (3748506)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1377501101:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.63/0.93 % (3748507)Refutation not found, incomplete strategy
% 0.63/0.93 % (3748507)------------------------------
% 0.63/0.93 % (3748507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.63/0.93 % (3748507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.93 % (3748507)CaDiCaL version: 2.1.3
% 0.63/0.93 % (3748507)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.93 % (3748507)Time elapsed: 0.002 s
% 0.63/0.93 % (3748507)Peak memory usage: 88 MB
% 0.63/0.93 % (3748507)Instructions burned: 1 (million)
% 0.63/0.93 % (3748506)Also succeeded, but the first one will report.
% 0.63/0.93 % (3748505)Refutation found. Thanks to Tanya!
% 0.63/0.93 % SZS status Theorem for theBenchmark
% 0.63/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.12 % (3748505)------------------------------
% 2.56/1.12 % (3748505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.12 % (3748505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.12 % (3748505)CaDiCaL version: 2.1.3
% 2.56/1.12 % (3748505)Termination reason: Refutation
% 2.56/1.12 % (3748505)Time elapsed: 0.002 s
% 2.56/1.12 % (3748505)Peak memory usage: 88 MB
% 2.56/1.12 % (3748505)Instructions burned: 6 (million)
% 2.56/1.12 % (3748505)------------------------------
% 2.56/1.12 % (3748505)------------------------------
% 2.56/1.12 % (3748496)Success in time 0.282 s
% 2.56/1.12 % Vampire exiting
%------------------------------------------------------------------------------