%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP019_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 11:35:27 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 3 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 10 con; 0-4 aty)
% Number of variables : 10 ( 9 !; 1 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_7,type,
tyop_2Enum_2Enum: $tType ).
tff(type_def_8,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(type_def_9,type,
tyop_2Erealax_2Ereal: $tType ).
tff(func_def_0,type,
app_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
combin_i_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).
tff(func_def_2,type,
combin_k_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).
tff(func_def_3,type,
combin_s_2E0:
!>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).
tff(func_def_4,type,
c_2Ebool_2E_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_5,type,
c_2Ebool_2E_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_6,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_7,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_8,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(func_def_9,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_10,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_11,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_12,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_13,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_14,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_15,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_16,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_17,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_18,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_19,type,
c_2Ecomplex_2Ecomplex__inv_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(func_def_20,type,
c_2Ecomplex_2Ecomplex__inv_2E1: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) > tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(func_def_21,type,
c_2Ecomplex_2Ecomplex__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(func_def_22,type,
c_2Ecomplex_2Ecomplex__of__num_2E1: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(func_def_23,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_24,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_25,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_26,type,
sK1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_27,type,
sK2:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_28,type,
sK3: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(f22,axiom,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1) ).
tff(f23,axiom,
! [X0: tyop_2Enum_2Enum] : ( c_2Ecomplex_2Ecomplex__of__num_2E1(X0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1) ).
tff(f28,axiom,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) = c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ( X0 = c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
tff(f29,conjecture,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( X0 != c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) )
=> ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) != c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
tff(f30,negated_conjecture,
~ ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( X0 != c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) )
=> ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) != c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
tff(f38,plain,
? [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) = c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) )
& ( X0 != c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) ) ),
inference(ennf_transformation,[],[f30]) ).
tff(f78,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] : ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E0,X0) ),
inference(cnf_transformation,[],[f22]) ).
tff(f79,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Ecomplex_2Ecomplex__of__num_2E1(X0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,X0) ),
inference(cnf_transformation,[],[f23]) ).
tff(f92,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) = X0 )
| ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) != c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) ) ),
inference(cnf_transformation,[],[f28]) ).
tff(f93,plain,
c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) != sK3,
inference(cnf_transformation,[],[f38]) ).
tff(f94,plain,
c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) = c_2Ecomplex_2Ecomplex__inv_2E1(sK3),
inference(cnf_transformation,[],[f38]) ).
tff(f99,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E0,X0) != app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,c_2Enum_2E0_2E0) )
| ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,c_2Enum_2E0_2E0) = X0 ) ),
inference(definition_unfolding,[],[f92,f79,f78,f79]) ).
tff(f101,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,c_2Enum_2E0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv_2E0,sK3),
inference(definition_unfolding,[],[f94,f79,f78]) ).
tff(f102,plain,
sK3 != app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,c_2Enum_2E0_2E0),
inference(definition_unfolding,[],[f93,f79]) ).
tff(f965,plain,
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,c_2Enum_2E0_2E0) != app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,c_2Enum_2E0_2E0) )
| ( sK3 = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,c_2Enum_2E0_2E0) ) ),
inference(superposition,[],[f99,f101]) ).
tff(f966,plain,
sK3 = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num_2E0,c_2Enum_2E0_2E0),
inference(trivial_inequality_removal,[],[f965]) ).
tff(f967,plain,
$false,
inference(forward_subsumption_resolution,[],[f966,f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP019_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 12:06:00 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.17/0.47 % (1919511)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1919520)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3975549847:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (1919517)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1919516)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3367290320_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (1919517)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2139799435:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1919518)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3836606689:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (1919519)dis+10_1_sil=32000:sp=arity:random_seed=1036394373:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1919521)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=722318862:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1919522)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1708095175:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % Exception at run slice level
% 0.17/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.47 % (1919520) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1919511-1919520"...
% 0.17/0.47 % (1919520)...printing done.
% 0.17/0.47 % (1919520)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1919520)------------------------------
% 0.17/0.47 % (1919520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1919520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1919520)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1919520)Termination reason: Refutation
% 0.17/0.47 % (1919520)Time elapsed: 0.016 s
% 0.17/0.47 % (1919520)Peak memory usage: 12 MB
% 0.17/0.47 % (1919520)Instructions burned: 46 (million)
% 0.17/0.47 % (1919511)Success in time 0.048 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------