%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP010_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 11:27:59 AM UTC 2026
% Result : Theorem 3.84s 1.62s
% Output : Refutation 3.84s
% 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 : 27 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 8 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 8 con; 0-4 aty)
% Number of variables : 24 ( 16 !; 8 ?; 24 :)
% 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,
sK9: $tType ).
tff(type_def_8,type,
sK10: $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_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_9,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_10,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_11,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_12,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_13,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_14,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_15,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_16,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_17,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_18,type,
c_2Ecardinal_2Ecardleq_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(func_def_19,type,
c_2Ecardinal_2Ecardleq_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_20,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_21,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_22,type,
sK6:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_23,type,
sK7:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_24,type,
sK8:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_25,type,
sK11: tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool) ).
tff(func_def_26,type,
sK12: tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP0: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP1: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP3: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP4: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP5: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_8,type,
sQ13_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f22,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(X0,X1),X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).
tff(f40,conjecture,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3))
<=> ~ p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
tff(f41,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3))
<=> ~ p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3)) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
tff(f58,plain,
? [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3))
<~> ~ p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3)) ),
inference(ennf_transformation,[],[f41]) ).
tff(f125,plain,
? [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3))
| p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3)) )
& ( ~ p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3))
| ~ p(c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f58]) ).
tff(f126,plain,
( ( p(c_2Ecardinal_2Ecardleq_2E2(sK9,sK10,sK11,sK12))
| p(c_2Ecardinal_2Ecardleq_2E2(sK9,sK10,sK11,sK12)) )
& ( ~ p(c_2Ecardinal_2Ecardleq_2E2(sK9,sK10,sK11,sK12))
| ~ p(c_2Ecardinal_2Ecardleq_2E2(sK9,sK10,sK11,sK12)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f125]) ).
tff(f166,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(X0,X1,X2,X3) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(X0,X1),X2),X3) ),
inference(cnf_transformation,[],[f22]) ).
tff(f261,plain,
( ~ p(c_2Ecardinal_2Ecardleq_2E2(sK9,sK10,sK11,sK12))
| ~ p(c_2Ecardinal_2Ecardleq_2E2(sK9,sK10,sK11,sK12)) ),
inference(cnf_transformation,[],[f126]) ).
tff(f262,plain,
( p(c_2Ecardinal_2Ecardleq_2E2(sK9,sK10,sK11,sK12))
| p(c_2Ecardinal_2Ecardleq_2E2(sK9,sK10,sK11,sK12)) ),
inference(cnf_transformation,[],[f126]) ).
tff(f269,plain,
( p(app_2E2(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(sK9,sK10),sK11),sK12))
| p(app_2E2(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(sK9,sK10),sK11),sK12)) ),
inference(definition_unfolding,[],[f262,f166,f166]) ).
tff(f270,plain,
( ~ p(app_2E2(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(sK9,sK10),sK11),sK12))
| ~ p(app_2E2(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(sK9,sK10),sK11),sK12)) ),
inference(definition_unfolding,[],[f261,f166,f166]) ).
tff(f300,plain,
~ p(app_2E2(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(sK9,sK10),sK11),sK12)),
inference(duplicate_literal_removal,[],[f270]) ).
tff(f301,plain,
p(app_2E2(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK9,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK10,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(sK9,sK10),sK11),sK12)),
inference(duplicate_literal_removal,[],[f269]) ).
tff(f357,plain,
$false,
inference(resolution,[],[f301,f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n020.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 27 11:57:50 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.84/1.62 % (3246404)Detected formulas, will run a generic FOF schedule.
% 3.84/1.62 % (3246417)dis-21_1_sil=8000:lcm=predicate:random_seed=1309249249: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)
% 3.84/1.62 % (3246417)First to succeed.
% 3.84/1.62 % (3246417)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3246404"
% 3.84/1.62 % (3246416)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2009905927:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.84/1.62 % (3246416)Also succeeded, but the first one will report.
% 3.84/1.62 % (3246415)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1550912372:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.84/1.62 % (3246411)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=4275381113:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.84/1.62 % (3246414)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2820479412:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.84/1.62 % (3246413)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=1664850652:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.84/1.62 % (3246412)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=935655940:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.84/1.62 % (3246414)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.84/1.62 % (3246415)Also succeeded, but the first one will report.
% 3.84/1.62 % (3246414)Also succeeded, but the first one will report.
% 3.84/1.62 % (3246413)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.84/1.62 % (3246417)Refutation found. Thanks to Tanya!
% 3.84/1.62 % SZS status Theorem for theBenchmark
% 3.84/1.62 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.62 % (3246417)------------------------------
% 3.84/1.62 % (3246417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.62 % (3246417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.62 % (3246417)CaDiCaL version: 2.1.3
% 3.84/1.62 % (3246417)Termination reason: Refutation
% 3.84/1.62 % (3246417)Time elapsed: 0.003 s
% 3.84/1.62 % (3246417)Peak memory usage: 88 MB
% 3.84/1.62 % (3246417)Instructions burned: 5 (million)
% 3.84/1.62 % (3246417)------------------------------
% 3.84/1.62 % (3246417)------------------------------
% 3.84/1.62 % (3246404)Success in time 0.432 s
% 3.84/1.62 % Vampire exiting
%------------------------------------------------------------------------------