%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n018.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 11:28:31 AM UTC 2026
% Result : Theorem 3.48s 1.45s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 5 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 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 : 29 ( 29 usr; 10 con; 0-4 aty)
% Number of variables : 8 ( 7 !; 1 ?; 8 :)
% 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: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(func_def_26,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
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(f33,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(f36,plain,
( ( c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) = c_2Ecomplex_2Ecomplex__inv_2E1(sK0) )
& ( c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) != sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f33]) ).
tff(f39,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) )
| ( c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) != X0 ) )
& ( ( 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(nnf_transformation,[],[f28]) ).
tff(f42,plain,
c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) != sK0,
inference(cnf_transformation,[],[f36]) ).
tff(f43,plain,
c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) = c_2Ecomplex_2Ecomplex__inv_2E1(sK0),
inference(cnf_transformation,[],[f36]) ).
tff(f47,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,[],[f39]) ).
tff(f52,plain,
sK0 != c_2Ecomplex_2Ecomplex__inv_2E1(sK0),
inference(superposition,[],[f42,f43]) ).
tff(f54,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( c_2Ecomplex_2Ecomplex__inv_2E1(sK0) = X0 )
| ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) != c_2Ecomplex_2Ecomplex__of__num_2E1(c_2Enum_2E0_2E0) ) ),
inference(forward_demodulation,[],[f47,f43]) ).
tff(f55,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( c_2Ecomplex_2Ecomplex__inv_2E1(X0) != c_2Ecomplex_2Ecomplex__inv_2E1(sK0) )
| ( c_2Ecomplex_2Ecomplex__inv_2E1(sK0) = X0 ) ),
inference(forward_demodulation,[],[f54,f43]) ).
tff(f56,plain,
sK0 = c_2Ecomplex_2Ecomplex__inv_2E1(sK0),
inference(equality_resolution,[],[f55]) ).
tff(f57,plain,
$false,
inference(forward_subsumption_resolution,[],[f56,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 12:07:39 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.48/1.45 % (2227660)Detected formulas, will run a generic FOF schedule.
% 3.48/1.45 % (2227761)dis-21_1_sil=8000:lcm=predicate:random_seed=2205785299: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)
% 3.48/1.45 % (2227761)Instruction limit reached!
% 3.48/1.45 % (2227761)------------------------------
% 3.48/1.45 % (2227761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.45 % (2227761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.45 % (2227761)CaDiCaL version: 2.1.3
% 3.48/1.45 % (2227761)Termination reason: Instruction limit
% 3.48/1.45 % (2227761)Termination phase: Saturation
% 3.48/1.45 % (2227761)Time elapsed: 0.035 s
% 3.48/1.45 % (2227761)Peak memory usage: 89 MB
% 3.48/1.45 % (2227761)Instructions burned: 131 (million)
% 3.48/1.45 % (2227759)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3991605436:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.45 % (2227755)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=3503458526:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.45 % (2227757)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=761073166:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.45 % (2227758)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=39975172:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.45 % (2227756)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=1110136742:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.45 % (2227758)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.48/1.45 % (2227757)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.48/1.45 % (2227759)First to succeed.
% 3.48/1.45 % (2227758)Also succeeded, but the first one will report.
% 3.48/1.45 % (2227759)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2227660"
% 3.48/1.45 % (2227760)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1542373178:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.45 % (2227760)Also succeeded, but the first one will report.
% 3.48/1.45 % (2227763)lrs+10_1_sil=8000:sp=occurrence:random_seed=2063744590:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.48/1.45 % (2227763)Also succeeded, but the first one will report.
% 3.48/1.45 % (2227759)Refutation found. Thanks to Tanya!
% 3.48/1.45 % SZS status Theorem for theBenchmark
% 3.48/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.45 % (2227759)------------------------------
% 3.48/1.45 % (2227759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.45 % (2227759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.45 % (2227759)CaDiCaL version: 2.1.3
% 3.48/1.45 % (2227759)Termination reason: Refutation
% 3.48/1.45 % (2227759)Time elapsed: 0.002 s
% 3.48/1.45 % (2227759)Peak memory usage: 88 MB
% 3.48/1.45 % (2227759)Instructions burned: 1 (million)
% 3.48/1.45 % (2227759)------------------------------
% 3.48/1.45 % (2227759)------------------------------
% 3.48/1.45 % (2227660)Success in time 0.402 s
% 3.48/1.45 % Vampire exiting
%------------------------------------------------------------------------------