%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT056^1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 : Wed Sep 30 07:48:54 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 99 ( 53 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 554 ( 41 ~; 37 |; 4 &; 462 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 72 !; 20 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
lst: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
ap: lst > lst > lst ).
thf(func_def_1,type,
cns: a > lst > lst ).
thf(func_def_2,type,
nl: lst ).
thf(func_def_3,type,
xs: lst ).
thf(func_def_5,type,
sK0: a ).
thf(func_def_6,type,
sK1: lst ).
thf(func_def_7,type,
sK2: lst ).
thf(func_def_8,type,
sK3: lst ).
thf(func_def_9,type,
sK4: lst ).
thf(func_def_10,type,
sK5: lst ).
thf(func_def_11,type,
sK6: lst ).
thf(func_def_12,type,
sK7: lst ).
thf(f1,axiom,
! [X0: lst] :
( ! [X1: lst,X2: lst] :
( ( ap @ nl @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ nl @ X1 ) @ X2 ) )
=> ( ! [X3: a,X4: lst] :
( ! [X5: lst,X6: lst] :
( ( ap @ X4 @ ( ap @ X5 @ X6 ) )
= ( ap @ ( ap @ X4 @ X5 ) @ X6 ) )
=> ! [X1: lst,X2: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X1 ) @ X2 ) ) )
=> ! [X5: lst,X6: lst] :
( ( ap @ X0 @ ( ap @ X5 @ X6 ) )
= ( ap @ ( ap @ X0 @ X5 ) @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093) ).
thf(f2,axiom,
! [X0: lst,X1: lst,X2: a] :
( ( ap @ ( cns @ X2 @ X1 ) @ X0 )
= ( cns @ X2 @ ( ap @ X1 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1p_Osimps_I2_J) ).
thf(f3,axiom,
! [X0: lst] :
( ( ap @ nl @ X0 )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2p_Osimps_I1_J) ).
thf(f4,conjecture,
! [X0: lst,X1: lst] :
( ( ap @ xs @ ( ap @ X0 @ X1 ) )
= ( ap @ ( ap @ xs @ X0 ) @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f5,negated_conjecture,
~ ! [X0: lst,X1: lst] :
( ( ap @ xs @ ( ap @ X0 @ X1 ) )
= ( ap @ ( ap @ xs @ X0 ) @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: lst] :
( ! [X1: lst,X2: lst] :
( ( ap @ nl @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ nl @ X1 ) @ X2 ) )
=> ( ! [X3: a,X4: lst] :
( ! [X5: lst,X6: lst] :
( ( ap @ X4 @ ( ap @ X5 @ X6 ) )
= ( ap @ ( ap @ X4 @ X5 ) @ X6 ) )
=> ! [X7: lst,X8: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X7 @ X8 ) )
= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X7 ) @ X8 ) ) )
=> ! [X9: lst,X10: lst] :
( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
! [X0: lst] :
( ! [X9: lst,X10: lst] :
( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) )
| ? [X3: a,X4: lst] :
( ? [X7: lst,X8: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X7 @ X8 ) )
!= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X7 ) @ X8 ) )
& ! [X5: lst,X6: lst] :
( ( ap @ X4 @ ( ap @ X5 @ X6 ) )
= ( ap @ ( ap @ X4 @ X5 ) @ X6 ) ) )
| ? [X1: lst,X2: lst] :
( ( ap @ nl @ ( ap @ X1 @ X2 ) )
!= ( ap @ ( ap @ nl @ X1 ) @ X2 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f8,plain,
! [X0: lst] :
( ! [X9: lst,X10: lst] :
( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) )
| ? [X3: a,X4: lst] :
( ? [X7: lst,X8: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X7 @ X8 ) )
!= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X7 ) @ X8 ) )
& ! [X5: lst,X6: lst] :
( ( ap @ X4 @ ( ap @ X5 @ X6 ) )
= ( ap @ ( ap @ X4 @ X5 ) @ X6 ) ) )
| ? [X1: lst,X2: lst] :
( ( ap @ nl @ ( ap @ X1 @ X2 ) )
!= ( ap @ ( ap @ nl @ X1 ) @ X2 ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
? [X0: lst,X1: lst] :
( ( ap @ xs @ ( ap @ X0 @ X1 ) )
!= ( ap @ ( ap @ xs @ X0 ) @ X1 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
! [X0: lst] :
( ! [X1: lst,X2: lst] :
( ( ap @ X0 @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ X0 @ X1 ) @ X2 ) )
| ? [X3: a,X4: lst] :
( ? [X5: lst,X6: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X5 @ X6 ) )
!= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X5 ) @ X6 ) )
& ! [X7: lst,X8: lst] :
( ( ap @ X4 @ ( ap @ X7 @ X8 ) )
= ( ap @ ( ap @ X4 @ X7 ) @ X8 ) ) )
| ? [X9: lst,X10: lst] :
( ( ap @ nl @ ( ap @ X9 @ X10 ) )
!= ( ap @ ( ap @ nl @ X9 ) @ X10 ) ) ),
inference(rectify,[],[f8]) ).
thf(f11,plain,
! [X0: lst] :
( ! [X1: lst,X2: lst] :
( ( ap @ X0 @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ X0 @ X1 ) @ X2 ) )
| ( ( ( ap @ ( cns @ sK0 @ sK1 ) @ ( ap @ sK2 @ sK3 ) )
!= ( ap @ ( ap @ ( cns @ sK0 @ sK1 ) @ sK2 ) @ sK3 ) )
& ! [X7: lst,X8: lst] :
( ( ap @ sK1 @ ( ap @ X7 @ X8 ) )
= ( ap @ ( ap @ sK1 @ X7 ) @ X8 ) ) )
| ( ( ap @ nl @ ( ap @ sK4 @ sK5 ) )
!= ( ap @ ( ap @ nl @ sK4 ) @ sK5 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3),skolemize(X9,sK4),skolemize(X10,sK5)],[f10]) ).
thf(f12,plain,
( ( ap @ xs @ ( ap @ sK6 @ sK7 ) )
!= ( ap @ ( ap @ xs @ sK6 ) @ sK7 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f9]) ).
thf(f13,plain,
! [X2: lst,X0: lst,X1: lst,X8: lst,X7: lst] :
( ( ( ap @ X0 @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ X0 @ X1 ) @ X2 ) )
| ( ( ap @ sK1 @ ( ap @ X7 @ X8 ) )
= ( ap @ ( ap @ sK1 @ X7 ) @ X8 ) )
| ( ( ap @ nl @ ( ap @ sK4 @ sK5 ) )
!= ( ap @ ( ap @ nl @ sK4 ) @ sK5 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
! [X2: lst,X0: lst,X1: lst] :
( ( ( ap @ X0 @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ X0 @ X1 ) @ X2 ) )
| ( ( ap @ ( cns @ sK0 @ sK1 ) @ ( ap @ sK2 @ sK3 ) )
!= ( ap @ ( ap @ ( cns @ sK0 @ sK1 ) @ sK2 ) @ sK3 ) )
| ( ( ap @ nl @ ( ap @ sK4 @ sK5 ) )
!= ( ap @ ( ap @ nl @ sK4 ) @ sK5 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
! [X2: a,X0: lst,X1: lst] :
( ( ap @ ( cns @ X2 @ X1 ) @ X0 )
= ( cns @ X2 @ ( ap @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f16,plain,
! [X0: lst] :
( ( ap @ nl @ X0 )
= X0 ),
inference(cnf_transformation,[],[f3]) ).
thf(f17,plain,
( ( ap @ xs @ ( ap @ sK6 @ sK7 ) )
!= ( ap @ ( ap @ xs @ sK6 ) @ sK7 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,definition,
( spl8_1
<=> ( ( ap @ nl @ ( ap @ sK4 @ sK5 ) )
= ( ap @ ( ap @ nl @ sK4 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f21,plain,
( ( ( ap @ nl @ ( ap @ sK4 @ sK5 ) )
!= ( ap @ ( ap @ nl @ sK4 ) @ sK5 ) )
| spl8_1 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f23,definition,
( spl8_2
<=> ! [X8: lst,X7: lst] :
( ( ap @ sK1 @ ( ap @ X7 @ X8 ) )
= ( ap @ ( ap @ sK1 @ X7 ) @ X8 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f24,plain,
( ! [X8: lst,X7: lst] :
( ( ap @ sK1 @ ( ap @ X7 @ X8 ) )
= ( ap @ ( ap @ sK1 @ X7 ) @ X8 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,definition,
( spl8_3
<=> ! [X2: lst,X0: lst,X1: lst] :
( ( ap @ X0 @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ X0 @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f27,plain,
( ! [X2: lst,X0: lst,X1: lst] :
( ( ap @ X0 @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ X0 @ X1 ) @ X2 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( ~ spl8_1
| spl8_2
| spl8_3 ),
inference(avatar_split_clause,[],[f13,f26,f23,f19]) ).
thf(f30,definition,
( spl8_4
<=> ( ( ap @ ( cns @ sK0 @ sK1 ) @ ( ap @ sK2 @ sK3 ) )
= ( ap @ ( ap @ ( cns @ sK0 @ sK1 ) @ sK2 ) @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f32,plain,
( ( ( ap @ ( cns @ sK0 @ sK1 ) @ ( ap @ sK2 @ sK3 ) )
!= ( ap @ ( ap @ ( cns @ sK0 @ sK1 ) @ sK2 ) @ sK3 ) )
| spl8_4 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( ~ spl8_1
| ~ spl8_4
| spl8_3 ),
inference(avatar_split_clause,[],[f14,f26,f30,f19]) ).
thf(f34,plain,
( ( ( ap @ sK4 @ sK5 )
!= ( ap @ nl @ ( ap @ sK4 @ sK5 ) ) )
| spl8_1 ),
inference(forward_demodulation,[],[f21,f16]) ).
thf(f35,plain,
( $false
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f34,f16]) ).
thf(f36,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f35]) ).
thf(f41,plain,
( ( ( ap @ xs @ ( ap @ sK6 @ sK7 ) )
!= ( ap @ xs @ ( ap @ sK6 @ sK7 ) ) )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f17,f27]) ).
thf(f42,plain,
( $false
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f43,plain,
~ spl8_3,
inference(avatar_contradiction_clause,[],[f42]) ).
thf(f48,plain,
( ( ( ap @ ( cns @ sK0 @ sK1 ) @ ( ap @ sK2 @ sK3 ) )
!= ( ap @ ( cns @ sK0 @ ( ap @ sK1 @ sK2 ) ) @ sK3 ) )
| spl8_4 ),
inference(forward_demodulation,[],[f32,f15]) ).
thf(f49,plain,
( ( ( ap @ ( cns @ sK0 @ sK1 ) @ ( ap @ sK2 @ sK3 ) )
!= ( cns @ sK0 @ ( ap @ ( ap @ sK1 @ sK2 ) @ sK3 ) ) )
| spl8_4 ),
inference(forward_demodulation,[],[f48,f15]) ).
thf(f50,plain,
( ( ( cns @ sK0 @ ( ap @ ( ap @ sK1 @ sK2 ) @ sK3 ) )
!= ( cns @ sK0 @ ( ap @ sK1 @ ( ap @ sK2 @ sK3 ) ) ) )
| spl8_4 ),
inference(forward_demodulation,[],[f49,f15]) ).
thf(f51,plain,
( ( ( cns @ sK0 @ ( ap @ sK1 @ ( ap @ sK2 @ sK3 ) ) )
!= ( cns @ sK0 @ ( ap @ sK1 @ ( ap @ sK2 @ sK3 ) ) ) )
| ~ spl8_2
| spl8_4 ),
inference(forward_demodulation,[],[f50,f24]) ).
thf(f52,plain,
( $false
| ~ spl8_2
| spl8_4 ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f53,plain,
( ~ spl8_2
| spl8_4 ),
inference(avatar_contradiction_clause,[],[f52]) ).
cnf(s1,plain,
( ~ spl8_1
| spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
( ~ spl8_1
| spl8_3
| ~ spl8_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
spl8_1,
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
~ spl8_3,
inference(sat_conversion,[],[f43]) ).
cnf(s5,plain,
( ~ spl8_2
| spl8_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s6,plain,
~ spl8_4,
inference(rat,[],[s2,s4,s3]) ).
cnf(s7,plain,
~ spl8_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s4,s7,s3]) ).
thf(f54,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT056^1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.16 % Computer : n008.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 17:58:55 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.23 % (3511798)Will run a generic schedule for satisfiability detection.
% 0.10/0.23 % (3511806)dis+10_1_sil=32000:sp=arity:random_seed=247217516:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.23 % (3511806) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3511798-3511806"...
% 0.10/0.23 % (3511806)...printing done.
% 0.10/0.23 % (3511804)% WARNING: option uhcvi not known.
% 0.10/0.23 % (3511806)Refutation found. Thanks to Tanya!
% 0.10/0.23 % SZS status Theorem for theBenchmark
% 0.10/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.23 % (3511806)------------------------------
% 0.10/0.23 % (3511806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.23 % (3511806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.23 % (3511806)CaDiCaL version: 2.1.3
% 0.10/0.23 % (3511806)Termination reason: Refutation
% 0.10/0.23 % (3511806)Time elapsed: 0.002 s
% 0.10/0.23 % (3511806)Peak memory usage: 12 MB
% 0.10/0.23 % (3511806)Instructions burned: 6 (million)
% 0.10/0.23 % (3511798)Success in time 0.027 s
% 0.10/0.23 % Vampire exiting
%------------------------------------------------------------------------------