%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP010_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 : n001.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 11:34:05 AM UTC 2026
% Result : Theorem 0.15s 0.63s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 9 ~; 0 |; 0 &)
% ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 8 con; 0-4 aty)
% Number of variables : 20 ( 16 !; 4 ?; 20 :)
% 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,
sK5: $tType ).
tff(type_def_8,type,
sK6: $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,
sK0:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_23,type,
sK1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_24,type,
sK2:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_25,type,
sK7: tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool) ).
tff(func_def_26,type,
sK8: tyop_2Emin_2Efun(sK6,tyop_2Emin_2Ebool) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP3: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP4: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $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/sandbox/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/sandbox/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(f98,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(f150,plain,
~ p(c_2Ecardinal_2Ecardleq_2E2(sK5,sK6,sK7,sK8)),
inference(cnf_transformation,[],[f58]) ).
tff(f151,plain,
p(c_2Ecardinal_2Ecardleq_2E2(sK5,sK6,sK7,sK8)),
inference(cnf_transformation,[],[f58]) ).
tff(f158,plain,
p(app_2E2(tyop_2Emin_2Efun(sK6,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK6,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(sK5,sK6),sK7),sK8)),
inference(definition_unfolding,[],[f151,f98]) ).
tff(f159,plain,
~ p(app_2E2(tyop_2Emin_2Efun(sK6,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(sK5,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK6,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(sK5,sK6),sK7),sK8)),
inference(definition_unfolding,[],[f150,f98]) ).
tff(f209,plain,
$false,
inference(forward_subsumption_resolution,[],[f159,f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.53 % Computer : n001.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.53 % CPULimit : 300
% 0.11/0.53 % WCLimit : 300
% 0.11/0.53 % DateTime : Sun Sep 27 12:02:47 UTC 2026
% 0.11/0.53 % CPUTime :
% 0.11/0.53 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.57 Running first-order model finding
% 0.15/0.57 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
% 0.15/0.63 % (3429530)Will run a generic schedule for satisfiability detection.
% 0.15/0.63 % (3429547)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=657117433_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.63 % Exception at run slice level
% 0.15/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.63 % (3429548)% WARNING: option uhcvi not known.
% 0.15/0.63 % (3429548)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1492096691:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.63 % (3429549)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=691126493:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.63 % (3429551)dis+10_1_sil=32000:sp=arity:random_seed=4206004172:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.63 % (3429552)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3080066775:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.63 % (3429553)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1059124487:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.63 % (3429554)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=196427523:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.63 % (3429549) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3429530-3429549"...
% 0.15/0.63 % (3429548) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3429530-3429548"...
% 0.15/0.63 % (3429553) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3429530-3429553"...
% 0.15/0.63 % (3429551) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3429530-3429551"...
% 0.15/0.63 % (3429552) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3429530-3429552"...
% 0.15/0.63 % (3429548)...printing done.
% 0.15/0.63 % (3429549)...printing done.
% 0.15/0.63 % (3429553)...printing done.
% 0.15/0.63 % (3429554) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3429530-3429554"...
% 0.15/0.63 % (3429552)...printing done.
% 0.15/0.63 % (3429551)...printing done.
% 0.15/0.63 % (3429563)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2744303836:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.15/0.63 % (3429548)Refutation found. Thanks to Tanya!
% 0.15/0.63 % SZS status Theorem for theBenchmark
% 0.15/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.63 % (3429548)------------------------------
% 0.15/0.63 % (3429548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.63 % (3429548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.63 % (3429548)CaDiCaL version: 2.1.3
% 0.15/0.63 % (3429548)Termination reason: Refutation
% 0.15/0.63 % (3429548)Time elapsed: 0.003 s
% 0.15/0.63 % (3429548)Peak memory usage: 12 MB
% 0.15/0.63 % (3429548)Instructions burned: 4 (million)
% 0.15/0.63 % (3429530)Success in time 0.047 s
% 0.15/0.63 % Vampire exiting
%------------------------------------------------------------------------------