%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN415+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 02:07:48 PM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 9 unt; 10 def)
% Number of atoms : 352 ( 47 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 380 ( 138 ~; 214 |; 10 &)
% ( 12 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 75 ( 0 sgn 67 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ? [X0] : f(X0)
& ! [X1,X2] :
( ( f(X1)
& f(X2) )
=> X1 = X2 ) )
<=> ? [X3] :
( f(X3)
& ! [X4] :
( f(X4)
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish317) ).
fof(f2,negated_conjecture,
~ ( ( ? [X0] : f(X0)
& ! [X1,X2] :
( ( f(X1)
& f(X2) )
=> X1 = X2 ) )
<=> ? [X3] :
( f(X3)
& ! [X4] :
( f(X4)
=> X3 = X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ? [X0] : f(X0)
& ! [X1,X2] :
( X1 = X2
| ~ f(X1)
| ~ f(X2) ) )
<~> ? [X3] :
( f(X3)
& ! [X4] :
( X3 = X4
| ~ f(X4) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ? [X0] : f(X0)
& ! [X1,X2] :
( X1 = X2
| ~ f(X1)
| ~ f(X2) ) )
<~> ? [X3] :
( f(X3)
& ! [X4] :
( X3 = X4
| ~ f(X4) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X4] :
( ~ f(X4)
| sK0 = X4
| f(sK3) ),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X2,X1,X4] :
( ~ f(X4)
| sK0 = X4
| ~ f(X2)
| ~ f(X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
! [X3,X0] :
( f(sK4(X3))
| ~ f(X3)
| sK1 != sK2
| ~ f(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f8,plain,
! [X3,X0] :
( sK4(X3) != X3
| ~ f(X3)
| sK1 != sK2
| ~ f(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f9,plain,
! [X3,X0] :
( f(sK4(X3))
| ~ f(X3)
| f(sK1)
| ~ f(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f10,plain,
! [X3,X0] :
( sK4(X3) != X3
| ~ f(X3)
| f(sK1)
| ~ f(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f11,plain,
! [X3,X0] :
( f(sK4(X3))
| ~ f(X3)
| f(sK2)
| ~ f(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f12,plain,
! [X3,X0] :
( sK4(X3) != X3
| ~ f(X3)
| f(sK2)
| ~ f(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f13,plain,
! [X2,X1] :
( f(sK0)
| ~ f(X2)
| ~ f(X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f14,plain,
( f(sK0)
| f(sK3) ),
inference(cnf_transformation,[],[f4]) ).
fof(f15,plain,
( ~ f(sK0)
| ~ f(sK3) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f16,plain,
! [X2,X1] :
( ~ f(sK0)
| f(X2)
| f(X1)
| X1 = X2 ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f17,plain,
! [X3,X0] :
( sK4(X3) != X3
| f(X3)
| ~ f(sK2)
| f(X0) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f18,plain,
! [X3,X0] :
( ~ f(sK4(X3))
| f(X3)
| ~ f(sK2)
| f(X0) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f19,plain,
! [X3,X0] :
( sK4(X3) != X3
| f(X3)
| ~ f(sK1)
| f(X0) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f20,plain,
! [X3,X0] :
( ~ f(sK4(X3))
| f(X3)
| ~ f(sK1)
| f(X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f21,plain,
! [X3,X0] :
( sK4(X3) != X3
| f(X3)
| sK1 != sK2
| f(X0) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f22,plain,
! [X3,X0] :
( ~ f(sK4(X3))
| f(X3)
| sK1 != sK2
| f(X0) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f23,plain,
! [X2,X1,X4] :
( f(X4)
| sK0 = X4
| f(X2)
| f(X1)
| X1 = X2 ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f24,plain,
! [X4] :
( f(X4)
| sK0 = X4
| ~ f(sK3) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f26,definition,
( spl5_1
<=> f(sK3) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f28,plain,
( ~ f(sK3)
| spl5_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f30,definition,
( spl5_2
<=> ! [X4] :
( f(X4)
| sK0 = X4 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f31,plain,
( ! [X4] :
( f(X4)
| sK0 = X4 )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f32,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f24,f30,f26]) ).
fof(f34,definition,
( spl5_3
<=> ! [X2,X1] :
( f(X2)
| f(X1)
| X1 = X2 ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f35,plain,
( ! [X2,X1] :
( f(X2)
| f(X1)
| X1 = X2 )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f23,f30,f34]) ).
fof(f38,definition,
( spl5_4
<=> ! [X0] : f(X0) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f39,plain,
( ! [X0] : f(X0)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl5_5
<=> sK1 = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f43,plain,
( sK1 != sK2
| spl5_5 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl5_6
<=> ! [X3] :
( ~ f(sK4(X3))
| f(X3) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f46,plain,
( ! [X3] :
( ~ f(sK4(X3))
| f(X3) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( spl5_4
| ~ spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f22,f45,f41,f38]) ).
fof(f49,definition,
( spl5_7
<=> ! [X3] :
( sK4(X3) != X3
| f(X3) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f50,plain,
( ! [X3] :
( sK4(X3) != X3
| f(X3) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( spl5_4
| ~ spl5_5
| spl5_7 ),
inference(avatar_split_clause,[],[f21,f49,f41,f38]) ).
fof(f53,definition,
( spl5_8
<=> f(sK1) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f55,plain,
( ~ f(sK1)
| spl5_8 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( spl5_4
| ~ spl5_8
| spl5_6 ),
inference(avatar_split_clause,[],[f20,f45,f53,f38]) ).
fof(f57,plain,
( spl5_4
| ~ spl5_8
| spl5_7 ),
inference(avatar_split_clause,[],[f19,f49,f53,f38]) ).
fof(f59,definition,
( spl5_9
<=> f(sK2) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f61,plain,
( ~ f(sK2)
| spl5_9 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( spl5_4
| ~ spl5_9
| spl5_6 ),
inference(avatar_split_clause,[],[f18,f45,f59,f38]) ).
fof(f63,plain,
( spl5_4
| ~ spl5_9
| spl5_7 ),
inference(avatar_split_clause,[],[f17,f49,f59,f38]) ).
fof(f65,definition,
( spl5_10
<=> f(sK0) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f67,plain,
( ~ f(sK0)
| spl5_10 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,plain,
( spl5_3
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f16,f65,f34]) ).
fof(f69,plain,
( ~ spl5_1
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f15,f65,f26]) ).
fof(f71,plain,
( sK0 = sK1
| ~ spl5_2
| spl5_8 ),
inference(resolution,[],[f31,f55]) ).
fof(f72,plain,
( sK0 = sK2
| ~ spl5_2
| spl5_9 ),
inference(resolution,[],[f31,f61]) ).
fof(f75,plain,
( sK0 != sK1
| ~ spl5_2
| spl5_5
| spl5_9 ),
inference(superposition,[],[f43,f72]) ).
fof(f77,plain,
( $false
| ~ spl5_2
| spl5_5
| spl5_8
| spl5_9 ),
inference(forward_subsumption_resolution,[],[f75,f71]) ).
fof(f78,plain,
( ~ spl5_2
| spl5_5
| spl5_8
| spl5_9 ),
inference(avatar_contradiction_clause,[],[f77]) ).
fof(f80,plain,
( $false
| ~ spl5_4
| spl5_10 ),
inference(backward_subsumption_resolution,[],[f67,f39]) ).
fof(f83,plain,
( $false
| spl5_1
| ~ spl5_4 ),
inference(backward_subsumption_resolution,[],[f28,f39]) ).
fof(f84,plain,
( ~ spl5_4
| spl5_10 ),
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f87,plain,
( spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f83]) ).
fof(f94,plain,
( ! [X0] :
( f(X0)
| sK0 = sK4(X0) )
| ~ spl5_2
| ~ spl5_6 ),
inference(resolution,[],[f46,f31]) ).
fof(f97,plain,
( sK0 = sK4(sK0)
| ~ spl5_2
| ~ spl5_6
| spl5_10 ),
inference(resolution,[],[f94,f67]) ).
fof(f100,plain,
( sK0 != sK0
| f(sK0)
| ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| spl5_10 ),
inference(superposition,[],[f50,f97]) ).
fof(f102,plain,
( f(sK0)
| ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| spl5_10 ),
inference(trivial_inequality_removal,[],[f100]) ).
fof(f103,plain,
( $false
| ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| spl5_10 ),
inference(forward_subsumption_resolution,[],[f102,f67]) ).
fof(f104,plain,
( ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| spl5_10 ),
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f107,plain,
( ! [X0] :
( f(X0)
| sK1 = X0 )
| ~ spl5_3
| spl5_8 ),
inference(resolution,[],[f35,f55]) ).
fof(f109,plain,
( ! [X0] :
( f(X0)
| sK3 = X0 )
| spl5_1
| ~ spl5_3 ),
inference(resolution,[],[f35,f28]) ).
fof(f110,plain,
( ! [X0,X1] :
( f(X1)
| f(X0)
| sK4(X0) = X1 )
| ~ spl5_3
| ~ spl5_6 ),
inference(resolution,[],[f35,f46]) ).
fof(f122,plain,
( sK1 = sK3
| spl5_1
| ~ spl5_3
| spl5_8 ),
inference(resolution,[],[f107,f28]) ).
fof(f125,plain,
( sK2 = sK3
| spl5_1
| ~ spl5_3
| spl5_9 ),
inference(resolution,[],[f109,f61]) ).
fof(f144,plain,
( ! [X0] :
( f(X0)
| sK4(X0) = X0 )
| ~ spl5_3
| ~ spl5_6 ),
inference(factoring,[],[f110]) ).
fof(f145,plain,
( ! [X0] : f(X0)
| ~ spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(forward_subsumption_resolution,[],[f144,f50]) ).
fof(f150,plain,
( spl5_4
| ~ spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f145,f49,f45,f34,f38]) ).
fof(f152,plain,
( sK1 = sK2
| spl5_1
| ~ spl5_3
| spl5_8
| spl5_9 ),
inference(forward_demodulation,[],[f125,f122]) ).
fof(f153,plain,
( spl5_5
| spl5_1
| ~ spl5_3
| spl5_8
| spl5_9 ),
inference(avatar_split_clause,[],[f152,f59,f53,f34,f26,f41]) ).
cnf(s1,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f36]) ).
cnf(s3,plain,
( spl5_4
| ~ spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f47]) ).
cnf(s4,plain,
( spl5_4
| ~ spl5_5
| spl5_7 ),
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
( spl5_4
| spl5_6
| ~ spl5_8 ),
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
( spl5_4
| spl5_7
| ~ spl5_8 ),
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
( spl5_4
| spl5_6
| ~ spl5_9 ),
inference(sat_conversion,[],[f62]) ).
cnf(s8,plain,
( spl5_4
| spl5_7
| ~ spl5_9 ),
inference(sat_conversion,[],[f63]) ).
cnf(s9,plain,
( spl5_3
| ~ spl5_10 ),
inference(sat_conversion,[],[f68]) ).
cnf(s10,plain,
( ~ spl5_1
| ~ spl5_10 ),
inference(sat_conversion,[],[f69]) ).
cnf(s11,plain,
( ~ spl5_2
| spl5_5
| spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f78]) ).
cnf(s12,plain,
( ~ spl5_4
| spl5_10 ),
inference(sat_conversion,[],[f84]) ).
cnf(s15,plain,
( spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f87]) ).
cnf(s18,plain,
( ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| spl5_10 ),
inference(sat_conversion,[],[f104]) ).
cnf(s21,plain,
( ~ spl5_3
| spl5_4
| ~ spl5_6
| ~ spl5_7 ),
inference(sat_conversion,[],[f150]) ).
cnf(s23,plain,
( spl5_1
| ~ spl5_3
| spl5_5
| spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f153]) ).
cnf(s24,plain,
( spl5_6
| spl5_5
| ~ spl5_3
| spl5_1 ),
inference(rat,[],[s23,s5,s7,s15]) ).
cnf(s25,plain,
( spl5_5
| ~ spl5_3
| spl5_1 ),
inference(rat,[],[s23,s6,s8,s21,s24,s15]) ).
cnf(s26,plain,
( ~ spl5_3
| spl5_1 ),
inference(rat,[],[s21,s3,s4,s25,s15]) ).
cnf(s27,plain,
( spl5_6
| spl5_5
| spl5_1 ),
inference(rat,[],[s11,s5,s7,s15,s2,s26]) ).
cnf(s28,plain,
( spl5_5
| spl5_1 ),
inference(rat,[],[s11,s6,s8,s18,s27,s15,s9,s2,s26]) ).
cnf(s29,plain,
spl5_1,
inference(rat,[],[s18,s3,s4,s28,s2,s9,s26,s15]) ).
cnf(s30,plain,
~ spl5_10,
inference(rat,[],[s10,s29]) ).
cnf(s31,plain,
spl5_2,
inference(rat,[],[s1,s29]) ).
cnf(s32,plain,
~ spl5_4,
inference(rat,[],[s12,s30]) ).
cnf(s33,plain,
( spl5_6
| spl5_5 ),
inference(rat,[],[s11,s5,s7,s31,s32]) ).
cnf(s34,plain,
spl5_5,
inference(rat,[],[s11,s6,s8,s18,s33,s31,s32,s30]) ).
cnf(s35,plain,
spl5_7,
inference(rat,[],[s4,s32,s34]) ).
cnf(s36,plain,
spl5_6,
inference(rat,[],[s3,s32,s34]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s18,s30,s31,s35,s36]) ).
fof(f154,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN415+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 15:55:03 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.25 % (2038421)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (2038430)% WARNING: option uhcvi not known.
% 0.07/0.25 % (2038430)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2828574971:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.07/0.25 % (2038430) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2038421-2038430"...
% 0.07/0.25 % (2038430)...printing done.
% 0.07/0.25 % (2038430)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (2038430)------------------------------
% 0.07/0.26 % (2038430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (2038430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (2038430)CaDiCaL version: 2.1.3
% 0.07/0.26 % (2038430)Termination reason: Refutation
% 0.07/0.26 % (2038430)Time elapsed: 0.003 s
% 0.07/0.26 % (2038430)Peak memory usage: 12 MB
% 0.07/0.26 % (2038430)Instructions burned: 5 (million)
% 0.07/0.26 % (2038421)Success in time 0.02 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------