%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COL094-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 : Thu Sep 24 12:09:35 PM UTC 2026
% Result : Unsatisfiable 56.39s 9.03s
% Output : CNFRefutation 56.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 23
% Syntax : Number of clauses : 138 ( 20 unt; 41 nHn; 138 RR)
% Number of literals : 330 ( 90 equ; 131 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 232 ( 63 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_parcontractE2,axiom,
( ~ member(pair(combS,X1),parcontract)
| X1 = combS ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_parcontractE2) ).
cnf(ap_parcontractE12,axiom,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE12) ).
cnf(ap_parcontractE1,axiom,
( ~ member(pair(comb_app(X1,X2),X3),parcontract)
| ap_parcontractE_c4(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c1(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE1) ).
cnf(app_app1,axiom,
( comb_app(X1,X2) != comb_app(X3,X4)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app1) ).
cnf(ap_parcontractE11,axiom,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE11) ).
cnf(s2_parcontractD_c1,negated_conjecture,
( ~ member(pair(q,X2),parcontract)
| ~ member(pair(p,X1),parcontract)
| r != comb_app(comb_app(combS,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_parcontractD_c1) ).
cnf(ap_parcontractE13,axiom,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE13) ).
cnf(ap_parcontractE14,axiom,
( ~ ap_parcontractE_c4(X1,X2,X3)
| X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE14) ).
cnf(ap_parcontractE3,axiom,
( ~ ap_parcontractE_c1(X1,X2,X3)
| X3 = comb_app(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE3) ).
cnf(s2_parcontractD_h1,hypothesis,
member(pair(comb_app(comb_app(combS,p),q),r),parcontract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_parcontractD_h1) ).
cnf(s_app,axiom,
combS != comb_app(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
cnf(ap_parcontractE2,axiom,
( ~ ap_parcontractE_c1(X1,X2,X3)
| member(comb_app(X1,X2),comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE2) ).
cnf(app_app2,axiom,
( comb_app(X1,X2) != comb_app(X3,X4)
| X2 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app2) ).
cnf(ap_parcontractE6,axiom,
( ~ ap_parcontractE_c2(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE6) ).
cnf(ap_parcontractE5,axiom,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X2,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE5) ).
cnf(ap_parcontractE4,axiom,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X3,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE4) ).
cnf(ap_parcontractE10,axiom,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X3 = comb_app(comb_app(ap_parcontractE_sk1p(X1,X2,X3),X2),comb_app(ap_parcontractE_sk1q(X1,X2,X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_parcontractE10) ).
cnf(parcontract_intros1,axiom,
( ~ member(X1,comb)
| member(pair(X1,X1),parcontract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parcontract_intros1) ).
cnf(ap_E1,axiom,
( ~ member(comb_app(X1,X2),comb)
| member(X1,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E1) ).
cnf(ap_E2,axiom,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_E2) ).
cnf(comb_intros3,axiom,
( ~ member(X2,comb)
| ~ member(X1,comb)
| member(comb_app(X1,X2),comb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros3) ).
cnf(comb_intros1,axiom,
member(combK,comb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comb_intros1) ).
cnf(k_s,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
cnf(c_0_23,plain,
( ~ member(pair(combS,X1),parcontract)
| X1 = combS ),
inference(fof_simplification,[status(thm)],[s_parcontractE2]) ).
cnf(c_0_24,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE12]) ).
cnf(c_0_25,plain,
( ~ member(pair(comb_app(X1,X2),X3),parcontract)
| ap_parcontractE_c4(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c1(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE1]) ).
cnf(c_0_26,plain,
( comb_app(X1,X2) != comb_app(X3,X4)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[app_app1]) ).
cnf(c_0_27,plain,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE11]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(pair(q,X2),parcontract)
| ~ member(pair(p,X1),parcontract)
| r != comb_app(comb_app(combS,X1),X2) ),
inference(fof_simplification,[status(thm)],[s2_parcontractD_c1]) ).
cnf(c_0_29,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE13]) ).
cnf(c_0_30,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE14]) ).
cnf(c_0_31,plain,
( ~ member(pair(combS,X1),parcontract)
| X1 = combS ),
c_0_23 ).
cnf(c_0_32,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract) ),
c_0_24 ).
cnf(c_0_33,plain,
( ~ ap_parcontractE_c1(X1,X2,X3)
| X3 = comb_app(X1,X2) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE3]) ).
cnf(c_0_34,plain,
( ~ member(pair(comb_app(X1,X2),X3),parcontract)
| ap_parcontractE_c4(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c1(X1,X2,X3) ),
c_0_25 ).
cnf(c_0_35,hypothesis,
member(pair(comb_app(comb_app(combS,p),q),r),parcontract),
s2_parcontractD_h1 ).
cnf(c_0_36,plain,
combS != comb_app(X1,X2),
inference(fof_simplification,[status(thm)],[s_app]) ).
cnf(c_0_37,plain,
( comb_app(X1,X2) != comb_app(X3,X4)
| X1 = X3 ),
c_0_26 ).
cnf(c_0_38,plain,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3)) ),
c_0_27 ).
cnf(c_0_39,negated_conjecture,
( ~ member(pair(q,X2),parcontract)
| ~ member(pair(p,X1),parcontract)
| r != comb_app(comb_app(combS,X1),X2) ),
c_0_28 ).
cnf(c_0_40,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract) ),
c_0_29 ).
cnf(c_0_41,plain,
( ~ ap_parcontractE_c4(X1,X2,X3)
| X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3)) ),
c_0_30 ).
cnf(c_0_42,plain,
( ~ ap_parcontractE_c4(combS,X1,X2)
| ap_parcontractE_sk2q(combS,X1,X2) = combS ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_43,plain,
( ~ ap_parcontractE_c1(X1,X2,X3)
| X3 = comb_app(X1,X2) ),
c_0_33 ).
cnf(c_0_44,hypothesis,
( ap_parcontractE_c1(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c3(comb_app(combS,p),q,r)
| ap_parcontractE_c4(comb_app(combS,p),q,r) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_45,plain,
combS != comb_app(X1,X2),
c_0_36 ).
cnf(c_0_46,plain,
( ~ ap_parcontractE_c3(comb_app(X1,X2),X3,X4)
| comb_app(combS,ap_parcontractE_sk1p(comb_app(X1,X2),X3,X4)) = X1 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_47,negated_conjecture,
( ~ member(pair(q,X3),parcontract)
| ~ ap_parcontractE_c4(X1,p,X2)
| comb_app(comb_app(combS,ap_parcontractE_sk2s(X1,p,X2)),X3) != r ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( ~ ap_parcontractE_c4(combS,X1,X2)
| comb_app(combS,ap_parcontractE_sk2s(combS,X1,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,hypothesis,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c3(comb_app(combS,p),q,r)
| ap_parcontractE_c4(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
~ ap_parcontractE_c3(comb_app(combS,X1),X2,X3),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(pair(q,X2),parcontract)
| ~ ap_parcontractE_c4(combS,p,X1)
| comb_app(X1,X2) != r ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
( ~ ap_parcontractE_c1(X1,X2,X3)
| member(comb_app(X1,X2),comb) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE2]) ).
cnf(c_0_53,plain,
( ~ ap_parcontractE_c4(comb_app(X1,X2),X3,X4)
| ap_parcontractE_c1(X1,X2,ap_parcontractE_sk2q(comb_app(X1,X2),X3,X4))
| ap_parcontractE_c2(X1,X2,ap_parcontractE_sk2q(comb_app(X1,X2),X3,X4))
| ap_parcontractE_c3(X1,X2,ap_parcontractE_sk2q(comb_app(X1,X2),X3,X4))
| ap_parcontractE_c4(X1,X2,ap_parcontractE_sk2q(comb_app(X1,X2),X3,X4)) ),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_54,hypothesis,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c4(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r ),
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
~ ap_parcontractE_c3(combS,X1,X2),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_38])]) ).
cnf(c_0_56,negated_conjecture,
( ~ ap_parcontractE_c4(X2,q,X3)
| ~ ap_parcontractE_c4(combS,p,X1)
| comb_app(X1,ap_parcontractE_sk2s(X2,q,X3)) != r ),
inference(spm,[status(thm)],[c_0_51,c_0_40]) ).
cnf(c_0_57,plain,
( ~ ap_parcontractE_c1(X1,X2,X3)
| member(comb_app(X1,X2),comb) ),
c_0_52 ).
cnf(c_0_58,hypothesis,
( ap_parcontractE_c1(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| comb_app(comb_app(combS,p),q) = r ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_59,plain,
( comb_app(X1,X2) != comb_app(X3,X4)
| X2 = X4 ),
inference(fof_simplification,[status(thm)],[app_app2]) ).
cnf(c_0_60,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE6]) ).
cnf(c_0_61,negated_conjecture,
( ~ ap_parcontractE_c4(X1,q,r)
| ~ ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(X1,q,r)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_41])]) ).
cnf(c_0_62,hypothesis,
( member(comb_app(combS,p),comb)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( comb_app(X1,X2) != comb_app(X3,X4)
| X2 = X4 ),
c_0_59 ).
cnf(c_0_64,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X2,comb) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE5]) ).
cnf(c_0_65,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| X1 = comb_app(combK,X3) ),
c_0_60 ).
cnf(c_0_66,negated_conjecture,
( member(comb_app(combS,p),comb)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| comb_app(comb_app(combS,p),q) = r ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_54]) ).
cnf(c_0_67,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X3,comb) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE4]) ).
cnf(c_0_68,plain,
( ~ ap_parcontractE_c4(X1,X2,comb_app(X3,X4))
| ap_parcontractE_sk2s(X1,X2,comb_app(X3,X4)) = X4 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_41])]) ).
cnf(c_0_69,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X2,comb) ),
c_0_64 ).
cnf(c_0_70,negated_conjecture,
( member(comb_app(combS,p),comb)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_45]) ).
cnf(c_0_71,plain,
( ~ ap_parcontractE_c4(X1,X2,comb_app(X3,X4))
| ap_parcontractE_sk2q(X1,X2,comb_app(X3,X4)) = X3 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_41])]) ).
cnf(c_0_72,plain,
( ~ ap_parcontractE_c2(X1,X2,X3)
| member(X3,comb) ),
c_0_67 ).
cnf(c_0_73,plain,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X3 = comb_app(comb_app(ap_parcontractE_sk1p(X1,X2,X3),X2),comb_app(ap_parcontractE_sk1q(X1,X2,X3),X2)) ),
inference(fof_simplification,[status(thm)],[ap_parcontractE10]) ).
cnf(c_0_74,plain,
( ~ ap_parcontractE_c4(X3,X1,comb_app(X4,X2))
| member(pair(X1,X2),parcontract) ),
inference(spm,[status(thm)],[c_0_40,c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( member(q,comb)
| member(comb_app(combS,p),comb)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,hypothesis,
( member(comb_app(comb_app(combS,p),q),comb)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c3(comb_app(combS,p),q,r)
| ap_parcontractE_c4(comb_app(combS,p),q,r) ),
inference(spm,[status(thm)],[c_0_57,c_0_44]) ).
cnf(c_0_77,plain,
( ~ member(X1,comb)
| member(pair(X1,X1),parcontract) ),
inference(fof_simplification,[status(thm)],[parcontract_intros1]) ).
cnf(c_0_78,plain,
( ~ member(comb_app(X1,X2),comb)
| member(X1,comb) ),
inference(fof_simplification,[status(thm)],[ap_E1]) ).
cnf(c_0_79,plain,
( ~ ap_parcontractE_c4(X1,X3,comb_app(X2,X4))
| member(pair(X1,X2),parcontract) ),
inference(spm,[status(thm)],[c_0_32,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( member(r,comb)
| member(comb_app(combS,p),comb)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_72,c_0_70]) ).
cnf(c_0_81,plain,
( ~ ap_parcontractE_c3(X1,X2,X3)
| X3 = comb_app(comb_app(ap_parcontractE_sk1p(X1,X2,X3),X2),comb_app(ap_parcontractE_sk1q(X1,X2,X3),X2)) ),
c_0_73 ).
cnf(c_0_82,negated_conjecture,
( ~ ap_parcontractE_c4(X2,X1,r)
| member(q,comb)
| member(pair(X1,q),parcontract)
| member(comb_app(combS,p),comb) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_83,hypothesis,
( member(comb_app(comb_app(combS,p),q),comb)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c4(comb_app(combS,p),q,r) ),
inference(sr,[status(thm)],[c_0_76,c_0_50]) ).
cnf(c_0_84,plain,
( ~ member(X1,comb)
| member(pair(X1,X1),parcontract) ),
c_0_77 ).
cnf(c_0_85,plain,
( ~ member(comb_app(X1,X2),comb)
| member(X1,comb) ),
c_0_78 ).
cnf(c_0_86,negated_conjecture,
( ~ ap_parcontractE_c4(X1,X2,r)
| member(r,comb)
| member(comb_app(combS,p),comb)
| member(pair(X1,comb_app(combS,p)),parcontract) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,plain,
( ~ ap_parcontractE_c3(X1,X2,comb_app(X3,X4))
| comb_app(ap_parcontractE_sk1p(X1,X2,comb_app(X3,X4)),X2) = X3 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_81])]) ).
cnf(c_0_88,hypothesis,
( member(comb_app(combS,p),comb)
| member(pair(q,q),parcontract)
| ap_parcontractE_c2(comb_app(combS,p),q,r) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_85]) ).
cnf(c_0_89,hypothesis,
( member(r,comb)
| member(comb_app(comb_app(combS,p),q),comb)
| member(pair(comb_app(combS,p),comb_app(combS,p)),parcontract) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_83]),c_0_84]),c_0_72]) ).
cnf(c_0_90,plain,
~ ap_parcontractE_c3(X1,X2,comb_app(combS,X3)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_87])]) ).
cnf(c_0_91,hypothesis,
( member(pair(q,q),parcontract)
| member(comb_app(combS,p),comb) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_88]),c_0_84]) ).
cnf(c_0_92,hypothesis,
( member(r,comb)
| member(comb_app(comb_app(combS,p),q),comb)
| ap_parcontractE_c1(combS,p,comb_app(combS,p))
| ap_parcontractE_c2(combS,p,comb_app(combS,p))
| ap_parcontractE_c4(combS,p,comb_app(combS,p)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_89]),c_0_90]) ).
cnf(c_0_93,plain,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
inference(fof_simplification,[status(thm)],[ap_E2]) ).
cnf(c_0_94,negated_conjecture,
( ~ ap_parcontractE_c4(combS,p,X1)
| comb_app(X1,q) != r
| member(comb_app(combS,p),comb) ),
inference(spm,[status(thm)],[c_0_51,c_0_91]) ).
cnf(c_0_95,hypothesis,
( member(r,comb)
| member(comb_app(combS,p),comb)
| ap_parcontractE_c4(combS,p,comb_app(combS,p)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_92]),c_0_85]),c_0_72]) ).
cnf(c_0_96,negated_conjecture,
( ~ member(p,comb)
| ~ member(pair(q,X1),parcontract)
| comb_app(comb_app(combS,p),X1) != r ),
inference(spm,[status(thm)],[c_0_39,c_0_84]) ).
cnf(c_0_97,negated_conjecture,
( member(comb_app(combS,p),comb)
| comb_app(combK,r) = comb_app(combS,p)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_65,c_0_70]) ).
cnf(c_0_98,plain,
( ~ member(comb_app(X1,X2),comb)
| member(X2,comb) ),
c_0_93 ).
cnf(c_0_99,negated_conjecture,
( member(r,comb)
| member(comb_app(combS,p),comb) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_80]) ).
cnf(c_0_100,negated_conjecture,
( ~ member(p,comb)
| comb_app(comb_app(combS,p),q) != r
| member(comb_app(combS,p),comb) ),
inference(spm,[status(thm)],[c_0_96,c_0_91]) ).
cnf(c_0_101,plain,
( ~ ap_parcontractE_c4(X2,X3,X4)
| ~ ap_parcontractE_c4(X5,X1,X4)
| member(pair(X1,ap_parcontractE_sk2s(X2,X3,X4)),parcontract) ),
inference(spm,[status(thm)],[c_0_74,c_0_41]) ).
cnf(c_0_102,negated_conjecture,
( ~ member(r,comb)
| member(comb_app(combS,p),comb)
| comb_app(combK,r) = comb_app(combS,p) ),
inference(spm,[status(thm)],[c_0_85,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( member(p,comb)
| member(r,comb) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( ~ member(p,comb)
| member(comb_app(combS,p),comb)
| comb_app(combK,r) = comb_app(combS,p) ),
inference(spm,[status(thm)],[c_0_100,c_0_97]) ).
cnf(c_0_105,hypothesis,
( ~ ap_parcontractE_c4(X1,X2,r)
| member(pair(q,ap_parcontractE_sk2s(X1,X2,r)),parcontract)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_101,c_0_54]) ).
cnf(c_0_106,plain,
( ~ member(X2,comb)
| ~ member(X1,comb)
| member(comb_app(X1,X2),comb) ),
inference(fof_simplification,[status(thm)],[comb_intros3]) ).
cnf(c_0_107,negated_conjecture,
( member(comb_app(combS,p),comb)
| comb_app(combK,r) = comb_app(combS,p) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]) ).
cnf(c_0_108,hypothesis,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_sk2q(comb_app(combS,p),q,r) = comb_app(combS,p) ),
inference(spm,[status(thm)],[c_0_43,c_0_58]) ).
cnf(c_0_109,hypothesis,
( member(pair(q,ap_parcontractE_sk2s(comb_app(combS,p),q,r)),parcontract)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_105,c_0_54]) ).
cnf(c_0_110,plain,
( ~ member(X2,comb)
| ~ member(X1,comb)
| member(comb_app(X1,X2),comb) ),
c_0_106 ).
cnf(c_0_111,negated_conjecture,
( member(p,comb)
| comb_app(combK,r) = comb_app(combS,p) ),
inference(spm,[status(thm)],[c_0_98,c_0_107]) ).
cnf(c_0_112,axiom,
member(combK,comb),
comb_intros1 ).
cnf(c_0_113,negated_conjecture,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_sk2q(comb_app(combS,p),q,r) = comb_app(combS,p) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_108]),c_0_54]) ).
cnf(c_0_114,negated_conjecture,
( ~ member(p,comb)
| comb_app(comb_app(combS,p),ap_parcontractE_sk2s(comb_app(combS,p),q,r)) != r
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_96,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
member(p,comb),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]),c_0_103]),c_0_98]) ).
cnf(c_0_116,negated_conjecture,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_sk2q(comb_app(combS,p),q,r) = comb_app(combS,p) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_113]),c_0_45]) ).
cnf(c_0_117,negated_conjecture,
( comb_app(comb_app(combS,p),ap_parcontractE_sk2s(comb_app(combS,p),q,r)) != r
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_118,negated_conjecture,
( ~ member(q,comb)
| ~ member(p,comb)
| comb_app(comb_app(combS,p),q) != r ),
inference(spm,[status(thm)],[c_0_96,c_0_84]) ).
cnf(c_0_119,negated_conjecture,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),q) = r ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_116]),c_0_54]),c_0_117]) ).
cnf(c_0_120,negated_conjecture,
( ~ member(q,comb)
| comb_app(comb_app(combS,p),q) != r ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_115])]) ).
cnf(c_0_121,negated_conjecture,
( comb_app(combK,r) = comb_app(combS,p)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_65,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( ~ member(q,comb)
| comb_app(combK,r) = comb_app(combS,p) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_123,plain,
combK != combS,
inference(fof_simplification,[status(thm)],[k_s]) ).
cnf(c_0_124,negated_conjecture,
( ~ member(p,comb)
| ~ ap_parcontractE_c4(X1,q,X2)
| comb_app(comb_app(combS,p),ap_parcontractE_sk2s(X1,q,X2)) != r ),
inference(spm,[status(thm)],[c_0_96,c_0_40]) ).
cnf(c_0_125,negated_conjecture,
( ~ member(q,comb)
| comb_app(combS,p) != comb_app(X1,X2)
| combK = X1 ),
inference(spm,[status(thm)],[c_0_37,c_0_122]) ).
cnf(c_0_126,plain,
combK != combS,
c_0_123 ).
cnf(c_0_127,negated_conjecture,
( ~ member(p,comb)
| ~ ap_parcontractE_c4(X2,q,comb_app(X3,X1))
| comb_app(comb_app(combS,p),X1) != r ),
inference(spm,[status(thm)],[c_0_124,c_0_68]) ).
cnf(c_0_128,negated_conjecture,
( member(q,comb)
| comb_app(comb_app(combS,p),q) = r ),
inference(spm,[status(thm)],[c_0_69,c_0_119]) ).
cnf(c_0_129,negated_conjecture,
~ member(q,comb),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_125]),c_0_126]) ).
cnf(c_0_130,negated_conjecture,
( ~ ap_parcontractE_c4(X2,q,comb_app(X3,X1))
| comb_app(comb_app(combS,p),X1) != r ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_115])]) ).
cnf(c_0_131,negated_conjecture,
comb_app(comb_app(combS,p),q) = r,
inference(sr,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_132,hypothesis,
( ap_parcontractE_c1(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c4(comb_app(combS,p),q,r) ),
inference(sr,[status(thm)],[c_0_44,c_0_50]) ).
cnf(c_0_133,negated_conjecture,
~ ap_parcontractE_c4(X1,q,r),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_131])]) ).
cnf(c_0_134,hypothesis,
( ap_parcontractE_c1(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r) ),
inference(sr,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_135,negated_conjecture,
~ member(r,comb),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_131]),c_0_129]) ).
cnf(c_0_136,hypothesis,
ap_parcontractE_c2(comb_app(combS,p),q,r),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_134]),c_0_131]),c_0_135]) ).
cnf(c_0_137,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_136]),c_0_135]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL094-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.46 % Computer : n002.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Mon Sep 21 14:12:33 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.52 Running first-order theorem proving
% 0.21/0.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 56.39/9.03 % Version: 3.5.1
% 56.39/9.03 % Preprocessing class: FSMSSMSMSSSNFFN.
% 56.39/9.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 56.39/9.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 56.39/9.03 % Starting new_bool_3 with 300s (1) cores
% 56.39/9.03 % Starting new_bool_1 with 300s (1) cores
% 56.39/9.03 % Starting sh5l with 300s (1) cores
% 56.39/9.03 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3481242 completed with status 0
% 56.39/9.03 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 56.39/9.03 % Preprocessing class: FSMSSMSMSSSNFFN.
% 56.39/9.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 56.39/9.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 56.39/9.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 56.39/9.03 % No SInE strategy applied
% 56.39/9.03 % Search class: FGHSF-FFMS32-MFFFFFNN
% 56.39/9.03 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 56.39/9.03 % Starting SubtermCWHack with 136s (1) cores
% 56.39/9.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 56.39/9.03 % Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 56.39/9.03 % Starting new_bool_3 with 136s (1) cores
% 56.39/9.03 % Starting new_bool_1 with 136s (1) cores
% 56.39/9.03 % G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 3481248 completed with status 0
% 56.39/9.03 % Result found by G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 56.39/9.03 % Preprocessing class: FSMSSMSMSSSNFFN.
% 56.39/9.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 56.39/9.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 56.39/9.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 56.39/9.03 % No SInE strategy applied
% 56.39/9.03 % Search class: FGHSF-FFMS32-MFFFFFNN
% 56.39/9.03 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 56.39/9.03 % Starting SubtermCWHack with 136s (1) cores
% 56.39/9.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 56.39/9.03 % Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 56.39/9.03 % Preprocessing time : 0.003 s
% 56.39/9.03 % Presaturation interreduction done
% 56.39/9.03
% 56.39/9.03 % Proof found!
% 56.39/9.03 % SZS status Unsatisfiable
% 56.39/9.03 % SZS output start CNFRefutation
% See solution above
% 56.39/9.03 % Parsed axioms : 55
% 56.39/9.03 % Removed by relevancy pruning/SinE : 0
% 56.39/9.03 % Initial clauses : 55
% 56.39/9.03 % Removed in clause preprocessing : 1
% 56.39/9.03 % Initial clauses in saturation : 54
% 56.39/9.03 % Processed clauses : 10862
% 56.39/9.03 % ...of these trivial : 10
% 56.39/9.03 % ...subsumed : 6205
% 56.39/9.03 % ...remaining for further processing : 4647
% 56.39/9.03 % Other redundant clauses eliminated : 1214
% 56.39/9.03 % Clauses deleted for lack of memory : 0
% 56.39/9.03 % Backward-subsumed : 946
% 56.39/9.03 % Backward-rewritten : 271
% 56.39/9.03 % Generated clauses : 124475
% 56.39/9.03 % ...of the previous two non-redundant : 122494
% 56.39/9.03 % ...aggressively subsumed : 0
% 56.39/9.03 % Contextual simplify-reflections : 214
% 56.39/9.03 % Paramodulations : 123215
% 56.39/9.03 % Factorizations : 0
% 56.39/9.03 % NegExts : 0
% 56.39/9.03 % Equation resolutions : 1222
% 56.39/9.03 % Disequality decompositions : 0
% 56.39/9.03 % Total rewrite steps : 2675
% 56.39/9.03 % ...of those cached : 2658
% 56.39/9.03 % Propositional unsat checks : 0
% 56.39/9.03 % Propositional check models : 0
% 56.39/9.03 % Propositional check unsatisfiable : 0
% 56.39/9.03 % Propositional clauses : 0
% 56.39/9.03 % Propositional clauses after purity: 0
% 56.39/9.03 % Propositional unsat core size : 0
% 56.39/9.03 % Propositional preprocessing time : 0.000
% 56.39/9.03 % Propositional encoding time : 0.000
% 56.39/9.03 % Propositional solver time : 0.000
% 56.39/9.03 % Success case prop preproc time : 0.000
% 56.39/9.03 % Success case prop encoding time : 0.000
% 56.39/9.03 % Success case prop solver time : 0.000
% 56.39/9.03 % Current number of processed clauses : 3340
% 56.39/9.03 % Positive orientable unit clauses : 17
% 56.39/9.03 % Positive unorientable unit clauses: 0
% 56.39/9.03 % Negative unit clauses : 49
% 56.39/9.03 % Non-unit-clauses : 3274
% 56.39/9.03 % Current number of unprocessed clauses: 109681
% 56.39/9.03 % ...number of literals in the above : 570035
% 56.39/9.03 % Current number of archived formulas : 0
% 56.39/9.03 % Current number of archived clauses : 1307
% 56.39/9.03 % Clause-clause subsumption calls (NU) : 4121143
% 56.39/9.03 % Rec. Clause-clause subsumption calls : 533325
% 56.39/9.03 % Non-unit clause-clause subsumptions : 5016
% 56.39/9.03 % Unit Clause-clause subsumption calls : 28790
% 56.39/9.03 % Rewrite failures with RHS unbound : 0
% 56.39/9.03 % BW rewrite match attempts : 64
% 56.39/9.03 % BW rewrite match successes : 10
% 56.39/9.03 % Condensation attempts : 0
% 56.39/9.03 % Condensation successes : 0
% 56.39/9.03 % Termbank termtop insertions : 2188209
% 56.39/9.03 % Search garbage collected termcells : 103
% 56.39/9.03
% 56.39/9.03 % -------------------------------------------------
% 56.39/9.03 % User time : 7.950 s
% 56.39/9.03 % System time : 0.176 s
% 56.39/9.03 % Total time : 8.126 s
% 56.39/9.03 % Maximum resident set size: 3420 pages
% 56.39/9.03
% 56.39/9.03 % -------------------------------------------------
% 56.39/9.03 % User time : 38.166 s
% 56.39/9.03 % System time : 1.816 s
% 56.39/9.03 % Total time : 39.982 s
% 56.39/9.03 % Maximum resident set size: 4864 pages
% 56.39/9.03 % E exiting
%------------------------------------------------------------------------------