%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL092-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 : Sun Sep 27 06:56:27 AM UTC 2026
% Result : Unsatisfiable 4.24s 2.27s
% Output : Refutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 55
% Syntax : Number of formulae : 111 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 235 ( 46 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1108 ( 124 ~; 124 |; 0 &; 860 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 8 con; 0-3 aty)
% Number of variables : 264 ( 0 ^; 264 !; 0 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
thf(r_decl,type,
r: $i ).
thf(comb_app_decl,type,
comb_app: $i > $i > $i ).
thf(combK_decl,type,
combK: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(parcontract_decl,type,
parcontract: $i ).
thf(comb_decl,type,
comb: $i ).
thf(ap_parcontractE_c4_decl,type,
ap_parcontractE_c4: $i > $i > $i > $o ).
thf(ap_parcontractE_sk2s_decl,type,
ap_parcontractE_sk2s: $i > $i > $i > $i ).
thf(ap_contractE_c3_decl,type,
ap_contractE_c3: $i > $i > $i > $o ).
thf(ap_contractE_sk2q_decl,type,
ap_contractE_sk2q: $i > $i > $i > $i ).
thf(ap_contractE_c4_decl,type,
ap_contractE_c4: $i > $i > $i > $o ).
thf(ap_contractE_sk3q_decl,type,
ap_contractE_sk3q: $i > $i > $i > $i ).
thf(contract_decl,type,
contract: $i ).
thf(ap_contractE_c2_decl,type,
ap_contractE_c2: $i > $i > $i > $o ).
thf(combS_decl,type,
combS: $i ).
thf(ap_contractE_sk1p_decl,type,
ap_contractE_sk1p: $i > $i > $i > $i ).
thf(ap_contractE_sk1q_decl,type,
ap_contractE_sk1q: $i > $i > $i > $i ).
thf(ap_parcontractE_c1_decl,type,
ap_parcontractE_c1: $i > $i > $i > $o ).
thf(ap_parcontractE_c2_decl,type,
ap_parcontractE_c2: $i > $i > $i > $o ).
thf(ap_parcontractE_c3_decl,type,
ap_parcontractE_c3: $i > $i > $i > $o ).
thf(ap_parcontractE_sk1q_decl,type,
ap_parcontractE_sk1q: $i > $i > $i > $i ).
thf(ap_parcontractE_sk1p_decl,type,
ap_parcontractE_sk1p: $i > $i > $i > $i ).
thf(rtrancl_decl,type,
rtrancl: $i > $i ).
thf(ap_parcontractE_sk2q_decl,type,
ap_parcontractE_sk2q: $i > $i > $i > $i ).
thf(ap_contractE_c1_decl,type,
ap_contractE_c1: $i > $i > $i > $o ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( parcontract @ ( A @ ( B @ ( A @ ( combK @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros2) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( parcontract @ ( A @ ( B @ ( A @ ( combK @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE2) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE14) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( A @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( combK @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE4) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( combK @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ap_contractE_c4 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c3 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c2 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c1 ) ) )
| ~ ( contract @ ( C @ ( B @ ( A @ comb_app ) @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE1) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ap_contractE_c4 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c3 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c2 ) ) )
| ( C @ ( B @ ( A @ ap_contractE_c1 ) ) )
| ~ ( contract @ ( C @ ( B @ ( A @ comb_app ) @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE5) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( contract @ ( A @ ( B @ ( A @ ( combK @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contract_K) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( contract @ ( A @ ( B @ ( A @ ( combK @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(5,axiom,
! [A: $i] :
( ( parcontract @ ( A @ ( A @ pair ) @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros1) ).
thf(67,plain,
! [A: $i] :
( ( parcontract @ ( A @ ( A @ pair ) @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE3) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_contractE_sk2q ) ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE12) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_contractE_sk2q ) ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,axiom,
! [A: $i] :
( ( comb @ ( combK @ member ) )
| ~ ( parcontract @ ( A @ ( combK @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_parcontractE1) ).
thf(138,plain,
! [A: $i] :
( ( comb @ ( combK @ member ) )
| ~ ( parcontract @ ( A @ ( combK @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( parcontract @ ( C @ ( B @ comb_app ) @ ( C @ ( A @ comb_app ) @ comb_app ) @ ( C @ ( B @ ( A @ ( combS @ comb_app ) @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( C @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros3) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( parcontract @ ( C @ ( B @ comb_app ) @ ( C @ ( A @ comb_app ) @ comb_app ) @ ( C @ ( B @ ( A @ ( combS @ comb_app ) @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( C @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( parcontract @ ( A @ ( p @ pair ) @ member ) )
| ( r
!= ( A @ ( combK @ comb_app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k1_parcontractD_c1) ).
thf(56,plain,
! [A: $i] :
( ~ ( parcontract @ ( A @ ( p @ pair ) @ member ) )
| ( r
!= ( A @ ( combK @ comb_app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( comb @ ( A @ member ) )
| ~ ( comb @ ( B @ ( A @ comb_app ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E1) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( comb @ ( A @ member ) )
| ~ ( comb @ ( B @ ( A @ comb_app ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( parcontract @ ( D @ ( B @ comb_app ) @ ( C @ ( A @ comb_app ) @ pair ) @ member ) )
| ~ ( parcontract @ ( D @ ( C @ pair ) @ member ) )
| ~ ( parcontract @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros4) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( parcontract @ ( D @ ( B @ comb_app ) @ ( C @ ( A @ comb_app ) @ pair ) @ member ) )
| ~ ( parcontract @ ( D @ ( C @ pair ) @ member ) )
| ~ ( parcontract @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( combS
!= ( B @ ( A @ comb_app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
thf(125,plain,
! [B: $i,A: $i] :
( combS
!= ( B @ ( A @ comb_app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE5) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE3) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( combK @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE6) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( combK @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE4) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ comb_app ) )
= ( D @ ( B @ comb_app ) ) )
| ( C != D )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app3) ).
thf(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ comb_app ) )
= ( D @ ( B @ comb_app ) ) )
| ( C != D )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ ap_contractE_sk3q ) ) @ ( A @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE15) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ ap_contractE_sk3q ) ) @ ( A @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ ( combS @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE9) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ ( combS @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app2) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( parcontract @ ( C @ ( B @ ( A @ ap_parcontractE_sk2q ) ) @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE12) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( parcontract @ ( C @ ( B @ ( A @ ap_parcontractE_sk2q ) ) @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_parcontractE_sk1p ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE7) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_parcontractE_sk1p ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( parcontract @ ( C @ ( B @ ( A @ ap_parcontractE_sk2s ) ) @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE13) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( parcontract @ ( C @ ( B @ ( A @ ap_parcontractE_sk2s ) ) @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE6) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,axiom,
! [A: $i] :
~ ( contract @ ( A @ ( combK @ pair ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_contractE) ).
thf(77,plain,
! [A: $i] :
~ ( contract @ ( A @ ( combK @ pair ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE9) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app1) ).
thf(176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ comb_app ) )
!= ( D @ ( C @ comb_app ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( comb @ ( B @ ( A @ comb_app ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros3) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( comb @ ( B @ ( A @ comb_app ) @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
thf(181,plain,
combK != combS,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_parcontractE_sk1q ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE8) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( C @ ( B @ ( A @ ap_parcontractE_sk1q ) ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(44,axiom,
comb @ ( combK @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros1) ).
thf(159,plain,
comb @ ( combK @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE7) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(11,axiom,
! [A: $i] :
( ( A = combS )
| ~ ( parcontract @ ( A @ ( combS @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_parcontractE2) ).
thf(81,plain,
! [A: $i] :
( ( A = combS )
| ~ ( parcontract @ ( A @ ( combS @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] :
( ( contract @ rtrancl @ ( A @ ( A @ pair ) @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduction_refl) ).
thf(98,plain,
! [A: $i] :
( ( contract @ rtrancl @ ( A @ ( A @ pair ) @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ ap_parcontractE_sk1q ) ) @ ( C @ ( B @ ( A @ ap_parcontractE_sk1p ) ) @ ( combS @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE11) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ ap_parcontractE_sk1q ) ) @ ( C @ ( B @ ( A @ ap_parcontractE_sk1p ) ) @ ( combS @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [A: $i] :
~ ( contract @ ( A @ ( combS @ pair ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_contractE) ).
thf(155,plain,
! [A: $i] :
~ ( contract @ ( A @ ( combS @ pair ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ ap_parcontractE_sk2s ) ) @ ( C @ ( B @ ( A @ ap_parcontractE_sk2q ) ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE14) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ ap_parcontractE_sk2s ) ) @ ( C @ ( B @ ( A @ ap_parcontractE_sk2q ) ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( comb @ ( B @ ( A @ comb_app ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E2) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( comb @ ( B @ ( A @ comb_app ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ ( A @ ap_contractE_sk3q ) ) @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE13) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ ( A @ ap_contractE_sk3q ) ) @ ( B @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( combK
!= ( B @ ( A @ comb_app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_app) ).
thf(143,plain,
! [B: $i,A: $i] :
( combK
!= ( B @ ( A @ comb_app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(55,axiom,
parcontract @ ( r @ ( p @ ( combK @ comb_app ) @ pair ) @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k1_parcontractD_h1) ).
thf(186,plain,
parcontract @ ( r @ ( p @ ( combK @ comb_app ) @ pair ) @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(26,axiom,
comb @ ( combS @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros2) ).
thf(114,plain,
comb @ ( combS @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ap_parcontractE_c4 ) ) )
| ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) )
| ( C @ ( B @ ( A @ ap_parcontractE_c2 ) ) )
| ( C @ ( B @ ( A @ ap_parcontractE_c1 ) ) )
| ~ ( parcontract @ ( C @ ( B @ ( A @ comb_app ) @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE1) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ap_parcontractE_c4 ) ) )
| ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) )
| ( C @ ( B @ ( A @ ap_parcontractE_c2 ) ) )
| ( C @ ( B @ ( A @ ap_parcontractE_c1 ) ) )
| ~ ( parcontract @ ( C @ ( B @ ( A @ comb_app ) @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_parcontractE_sk1q ) ) @ comb_app ) @ ( B @ ( C @ ( B @ ( A @ ap_parcontractE_sk1p ) ) @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE10) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_parcontractE_sk1q ) ) @ comb_app ) @ ( B @ ( C @ ( B @ ( A @ ap_parcontractE_sk1p ) ) @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE11) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ ( A @ comb_app ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE2) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( comb @ ( B @ ( A @ comb_app ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_parcontractE_c1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ comb_app ) @ ( C @ ( A @ comb_app ) @ comb_app ) @ ( C @ ( B @ ( A @ ( combS @ comb_app ) @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( C @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contract_S) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ comb_app ) @ ( C @ ( A @ comb_app ) @ comb_app ) @ ( C @ ( B @ ( A @ ( combS @ comb_app ) @ comb_app ) @ comb_app ) @ pair ) @ member ) )
| ~ ( comb @ ( C @ member ) )
| ~ ( comb @ ( B @ member ) )
| ~ ( comb @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ comb_app ) @ ( B @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE8) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( C @ ( B @ ( A @ ap_contractE_sk1q ) ) @ comb_app ) @ ( B @ ( C @ ( B @ ( A @ ap_contractE_sk1p ) ) @ comb_app ) @ comb_app ) ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ ( A @ ap_contractE_sk2q ) ) @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE10) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( contract @ ( C @ ( B @ ( A @ ap_contractE_sk2q ) ) @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ ap_contractE_c3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i] :
( ( comb @ ( combS @ member ) )
| ~ ( parcontract @ ( A @ ( combS @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_parcontractE1) ).
thf(90,plain,
! [A: $i] :
( ( comb @ ( combS @ member ) )
| ~ ( parcontract @ ( A @ ( combS @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [A: $i] :
( ( A = combK )
| ~ ( parcontract @ ( A @ ( combK @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_parcontractE2) ).
thf(111,plain,
! [A: $i] :
( ( A = combK )
| ~ ( parcontract @ ( A @ ( combK @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(205,plain,
$false,
inference(e,[status(thm)],[115,174,160,169,128,149,162,67,104,69,138,88,56,153,184,125,157,164,106,84,61,133,74,117,102,92,65,109,77,96,176,59,181,86,159,172,81,98,140,155,130,167,72,143,186,114,151,146,136,79,94,122,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL092-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n006.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 23:13:25 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.70/0.74 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.95/0.87 % [INFO] Parsing done (129ms).
% 0.95/0.87 % [INFO] Running in sequential loop mode.
% 1.58/1.07 % [INFO] eprover registered as external prover.
% 1.58/1.08 % [INFO] Scanning for conjecture ...
% 1.86/1.15 % [INFO] Found a conjecture (or negated_conjecture) and 54 axioms. Running axiom selection ...
% 1.95/1.24 % [INFO] Axiom selection finished. Selected 54 axioms (removed 0 axioms).
% 2.18/1.31 % [INFO] Problem is propositional (TPTP CNF).
% 2.18/1.32 % [INFO] Type checking passed.
% 2.18/1.32 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.24/2.27 % External prover 'e' found a proof!
% 4.24/2.27 % [INFO] Killing All external provers ...
% 4.24/2.27 % Time passed: 1779ms (effective reasoning time: 1393ms)
% 4.24/2.27 % Axioms used in derivation (54): comb_intros3, ap_parcontractE10, parcontract_intros2, ap_parcontractE7, ap_contractE4, ap_contractE11, k1_parcontractD_h1, parcontract_intros4, s_parcontractE1, ap_contractE9, ap_parcontractE13, ap_contractE7, ap_parcontractE14, ap_contractE10, app_app3, ap_parcontractE3, parcontract_intros3, ap_contractE2, k_parcontractE1, ap_contractE14, ap_parcontractE6, app_app2, s_app, k_s, ap_parcontractE1, ap_E1, k_contractE, ap_parcontractE11, ap_contractE15, ap_contractE1, ap_contractE8, s_parcontractE2, contract_K, app_app1, ap_parcontractE5, s_contractE, reduction_refl, ap_contractE12, ap_parcontractE2, ap_contractE5, ap_E2, comb_intros1, ap_parcontractE12, k_app, ap_parcontractE9, parcontract_intros1, contract_S, comb_intros2, ap_contractE6, ap_parcontractE4, ap_contractE13, k_parcontractE2, ap_parcontractE8, ap_contractE3
% 4.24/2.27 % No. of inferences in proof: 111
% 4.24/2.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1779 ms resp. 1393 ms w/o parsing
% 4.78/2.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.78/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------