%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL094-1 : TPTP v9.2.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:12:19 PM UTC 2026
% Result : Unsatisfiable 15.29s 9.59s
% Output : CNFRefutation 15.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 22
% Syntax : Number of clauses : 113 ( 17 unt; 40 nHn; 113 RR)
% Number of literals : 278 ( 74 equ; 103 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 : 166 ( 46 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_parcontractE2,axiom,
( X1 = combS
| ~ member(pair(combS,X1),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_parcontractE2) ).
cnf(ap_parcontractE12,axiom,
( member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE12) ).
cnf(ap_parcontractE1,axiom,
( ap_parcontractE_c1(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c4(X1,X2,X3)
| ~ member(pair(comb_app(X1,X2),X3),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE1) ).
cnf(s2_parcontractD_h1,hypothesis,
member(pair(comb_app(comb_app(combS,p),q),r),parcontract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_parcontractD_h1) ).
cnf(app_app1,axiom,
( X1 = X3
| comb_app(X1,X2) != comb_app(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app1) ).
cnf(ap_parcontractE11,axiom,
( X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3))
| ~ ap_parcontractE_c3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE11) ).
cnf(s2_parcontractD_c1,negated_conjecture,
( r != comb_app(comb_app(combS,X1),X2)
| ~ member(pair(p,X1),parcontract)
| ~ member(pair(q,X2),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_parcontractD_c1) ).
cnf(ap_parcontractE13,axiom,
( member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE13) ).
cnf(ap_parcontractE14,axiom,
( X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3))
| ~ ap_parcontractE_c4(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE14) ).
cnf(ap_parcontractE3,axiom,
( X3 = comb_app(X1,X2)
| ~ ap_parcontractE_c1(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE3) ).
cnf(s_app,axiom,
combS != comb_app(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
cnf(ap_parcontractE2,axiom,
( member(comb_app(X1,X2),comb)
| ~ ap_parcontractE_c1(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE2) ).
cnf(app_app2,axiom,
( X2 = X4
| comb_app(X1,X2) != comb_app(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app2) ).
cnf(ap_parcontractE6,axiom,
( X1 = comb_app(combK,X3)
| ~ ap_parcontractE_c2(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE6) ).
cnf(ap_parcontractE5,axiom,
( member(X2,comb)
| ~ ap_parcontractE_c2(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE5) ).
cnf(ap_parcontractE4,axiom,
( member(X3,comb)
| ~ ap_parcontractE_c2(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE4) ).
cnf(parcontract_intros1,axiom,
( member(pair(X1,X1),parcontract)
| ~ member(X1,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros1) ).
cnf(ap_E1,axiom,
( member(X1,comb)
| ~ member(comb_app(X1,X2),comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E1) ).
cnf(ap_E2,axiom,
( member(X2,comb)
| ~ member(comb_app(X1,X2),comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E2) ).
cnf(comb_intros3,axiom,
( member(comb_app(X1,X2),comb)
| ~ member(X1,comb)
| ~ member(X2,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros3) ).
cnf(comb_intros1,axiom,
member(combK,comb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros1) ).
cnf(k_s,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
cnf(c_0_22,axiom,
( X1 = combS
| ~ member(pair(combS,X1),parcontract) ),
s_parcontractE2 ).
cnf(c_0_23,axiom,
( member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
ap_parcontractE12 ).
cnf(c_0_24,axiom,
( ap_parcontractE_c1(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c4(X1,X2,X3)
| ~ member(pair(comb_app(X1,X2),X3),parcontract) ),
ap_parcontractE1 ).
cnf(c_0_25,hypothesis,
member(pair(comb_app(comb_app(combS,p),q),r),parcontract),
s2_parcontractD_h1 ).
cnf(c_0_26,axiom,
( X1 = X3
| comb_app(X1,X2) != comb_app(X3,X4) ),
app_app1 ).
cnf(c_0_27,axiom,
( X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3))
| ~ ap_parcontractE_c3(X1,X2,X3) ),
ap_parcontractE11 ).
cnf(c_0_28,negated_conjecture,
( r != comb_app(comb_app(combS,X1),X2)
| ~ member(pair(p,X1),parcontract)
| ~ member(pair(q,X2),parcontract) ),
s2_parcontractD_c1 ).
cnf(c_0_29,axiom,
( member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
ap_parcontractE13 ).
cnf(c_0_30,axiom,
( X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3))
| ~ ap_parcontractE_c4(X1,X2,X3) ),
ap_parcontractE14 ).
cnf(c_0_31,plain,
( ap_parcontractE_sk2q(combS,X1,X2) = combS
| ~ ap_parcontractE_c4(combS,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,axiom,
( X3 = comb_app(X1,X2)
| ~ ap_parcontractE_c1(X1,X2,X3) ),
ap_parcontractE3 ).
cnf(c_0_33,hypothesis,
( ap_parcontractE_c4(comb_app(combS,p),q,r)
| ap_parcontractE_c3(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c1(comb_app(combS,p),q,r) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,axiom,
combS != comb_app(X1,X2),
s_app ).
cnf(c_0_35,plain,
( comb_app(combS,ap_parcontractE_sk1p(comb_app(X1,X2),X3,X4)) = X1
| ~ ap_parcontractE_c3(comb_app(X1,X2),X3,X4) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_36,negated_conjecture,
( comb_app(comb_app(combS,ap_parcontractE_sk2s(X1,p,X2)),X3) != r
| ~ ap_parcontractE_c4(X1,p,X2)
| ~ member(pair(q,X3),parcontract) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
( comb_app(combS,ap_parcontractE_sk2s(combS,X1,X2)) = X2
| ~ ap_parcontractE_c4(combS,X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,hypothesis,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c4(comb_app(combS,p),q,r)
| ap_parcontractE_c3(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
~ ap_parcontractE_c3(comb_app(combS,X1),X2,X3),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_40,negated_conjecture,
( comb_app(X1,X2) != r
| ~ ap_parcontractE_c4(combS,p,X1)
| ~ member(pair(q,X2),parcontract) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
( ap_parcontractE_c4(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_c2(X1,X2,ap_parcontractE_sk2q(comb_app(X1,X2),X3,X4))
| ap_parcontractE_c1(X1,X2,ap_parcontractE_sk2q(comb_app(X1,X2),X3,X4))
| ~ ap_parcontractE_c4(comb_app(X1,X2),X3,X4) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_42,hypothesis,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c4(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r) ),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
~ ap_parcontractE_c3(combS,X1,X2),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27])]) ).
cnf(c_0_44,negated_conjecture,
( comb_app(X1,ap_parcontractE_sk2s(X2,q,X3)) != r
| ~ ap_parcontractE_c4(combS,p,X1)
| ~ ap_parcontractE_c4(X2,q,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_29]) ).
cnf(c_0_45,axiom,
( member(comb_app(X1,X2),comb)
| ~ ap_parcontractE_c1(X1,X2,X3) ),
ap_parcontractE2 ).
cnf(c_0_46,hypothesis,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c1(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( ~ ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(X1,q,r))
| ~ ap_parcontractE_c4(X1,q,r) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_30])]) ).
cnf(c_0_48,hypothesis,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| member(comb_app(combS,p),comb) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,axiom,
( X2 = X4
| comb_app(X1,X2) != comb_app(X3,X4) ),
app_app2 ).
cnf(c_0_50,axiom,
( X1 = comb_app(combK,X3)
| ~ ap_parcontractE_c2(X1,X2,X3) ),
ap_parcontractE6 ).
cnf(c_0_51,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| member(comb_app(combS,p),comb) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42]) ).
cnf(c_0_52,plain,
( ap_parcontractE_sk2s(X1,X2,comb_app(X3,X4)) = X4
| ~ ap_parcontractE_c4(X1,X2,comb_app(X3,X4)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_30])]) ).
cnf(c_0_53,axiom,
( member(X2,comb)
| ~ ap_parcontractE_c2(X1,X2,X3) ),
ap_parcontractE5 ).
cnf(c_0_54,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| member(comb_app(combS,p),comb) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_34]) ).
cnf(c_0_55,plain,
( ap_parcontractE_sk2q(X1,X2,comb_app(X3,X4)) = X3
| ~ ap_parcontractE_c4(X1,X2,comb_app(X3,X4)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30])]) ).
cnf(c_0_56,axiom,
( member(X3,comb)
| ~ ap_parcontractE_c2(X1,X2,X3) ),
ap_parcontractE4 ).
cnf(c_0_57,plain,
( member(pair(X1,X2),parcontract)
| ~ ap_parcontractE_c4(X3,X1,comb_app(X4,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| member(comb_app(combS,p),comb)
| member(q,comb) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,hypothesis,
( ap_parcontractE_c4(comb_app(combS,p),q,r)
| ap_parcontractE_c3(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| member(comb_app(comb_app(combS,p),q),comb) ),
inference(spm,[status(thm)],[c_0_45,c_0_33]) ).
cnf(c_0_60,plain,
( member(pair(X1,X2),parcontract)
| ~ ap_parcontractE_c4(X1,X3,comb_app(X2,X4)) ),
inference(spm,[status(thm)],[c_0_23,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| member(comb_app(combS,p),comb)
| member(r,comb) ),
inference(spm,[status(thm)],[c_0_56,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( member(comb_app(combS,p),comb)
| member(pair(X1,q),parcontract)
| member(q,comb)
| ~ ap_parcontractE_c4(X2,X1,r) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,hypothesis,
( ap_parcontractE_c4(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| member(comb_app(comb_app(combS,p),q),comb) ),
inference(sr,[status(thm)],[c_0_59,c_0_39]) ).
cnf(c_0_64,axiom,
( member(pair(X1,X1),parcontract)
| ~ member(X1,comb) ),
parcontract_intros1 ).
cnf(c_0_65,axiom,
( member(X1,comb)
| ~ member(comb_app(X1,X2),comb) ),
ap_E1 ).
cnf(c_0_66,negated_conjecture,
( member(pair(X1,comb_app(combS,p)),parcontract)
| member(comb_app(combS,p),comb)
| member(r,comb)
| ~ ap_parcontractE_c4(X1,X2,r) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,hypothesis,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| member(pair(q,q),parcontract)
| member(comb_app(combS,p),comb) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65]) ).
cnf(c_0_68,hypothesis,
( member(pair(comb_app(combS,p),comb_app(combS,p)),parcontract)
| member(comb_app(comb_app(combS,p),q),comb)
| member(r,comb) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_63]),c_0_64]),c_0_56]) ).
cnf(c_0_69,hypothesis,
( member(comb_app(combS,p),comb)
| member(pair(q,q),parcontract) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_67]),c_0_64]) ).
cnf(c_0_70,hypothesis,
( ap_parcontractE_c4(combS,p,comb_app(combS,p))
| ap_parcontractE_c2(combS,p,comb_app(combS,p))
| ap_parcontractE_c1(combS,p,comb_app(combS,p))
| member(comb_app(comb_app(combS,p),q),comb)
| member(r,comb) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_68]),c_0_43]) ).
cnf(c_0_71,negated_conjecture,
( member(comb_app(combS,p),comb)
| comb_app(X1,q) != r
| ~ ap_parcontractE_c4(combS,p,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_69]) ).
cnf(c_0_72,hypothesis,
( ap_parcontractE_c4(combS,p,comb_app(combS,p))
| member(comb_app(combS,p),comb)
| member(r,comb) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_70]),c_0_65]),c_0_56]) ).
cnf(c_0_73,negated_conjecture,
( comb_app(comb_app(combS,p),X1) != r
| ~ member(pair(q,X1),parcontract)
| ~ member(p,comb) ),
inference(spm,[status(thm)],[c_0_28,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| comb_app(combK,r) = comb_app(combS,p)
| member(comb_app(combS,p),comb) ),
inference(spm,[status(thm)],[c_0_50,c_0_54]) ).
cnf(c_0_75,axiom,
( member(X2,comb)
| ~ member(comb_app(X1,X2),comb) ),
ap_E2 ).
cnf(c_0_76,negated_conjecture,
( member(comb_app(combS,p),comb)
| member(r,comb) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_61]) ).
cnf(c_0_77,negated_conjecture,
( member(comb_app(combS,p),comb)
| comb_app(comb_app(combS,p),q) != r
| ~ member(p,comb) ),
inference(spm,[status(thm)],[c_0_73,c_0_69]) ).
cnf(c_0_78,plain,
( member(pair(X1,ap_parcontractE_sk2s(X2,X3,X4)),parcontract)
| ~ ap_parcontractE_c4(X5,X1,X4)
| ~ ap_parcontractE_c4(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_57,c_0_30]) ).
cnf(c_0_79,negated_conjecture,
( comb_app(combK,r) = comb_app(combS,p)
| member(comb_app(combS,p),comb)
| ~ member(r,comb) ),
inference(spm,[status(thm)],[c_0_65,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( member(r,comb)
| member(p,comb) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( comb_app(combK,r) = comb_app(combS,p)
| member(comb_app(combS,p),comb)
| ~ member(p,comb) ),
inference(spm,[status(thm)],[c_0_77,c_0_74]) ).
cnf(c_0_82,hypothesis,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| member(pair(q,ap_parcontractE_sk2s(X1,X2,r)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,r) ),
inference(spm,[status(thm)],[c_0_78,c_0_42]) ).
cnf(c_0_83,negated_conjecture,
( comb_app(combK,r) = comb_app(combS,p)
| member(comb_app(combS,p),comb) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_84,hypothesis,
( ap_parcontractE_sk2q(comb_app(combS,p),q,r) = comb_app(combS,p)
| comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c4(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(comb_app(combS,p),q,r) ),
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
cnf(c_0_85,hypothesis,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| member(pair(q,ap_parcontractE_sk2s(comb_app(combS,p),q,r)),parcontract) ),
inference(spm,[status(thm)],[c_0_82,c_0_42]) ).
cnf(c_0_86,axiom,
( member(comb_app(X1,X2),comb)
| ~ member(X1,comb)
| ~ member(X2,comb) ),
comb_intros3 ).
cnf(c_0_87,negated_conjecture,
( comb_app(combK,r) = comb_app(combS,p)
| member(p,comb) ),
inference(spm,[status(thm)],[c_0_75,c_0_83]) ).
cnf(c_0_88,axiom,
member(combK,comb),
comb_intros1 ).
cnf(c_0_89,negated_conjecture,
( ap_parcontractE_sk2q(comb_app(combS,p),q,r) = comb_app(combS,p)
| comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(combS,p,ap_parcontractE_sk2q(comb_app(combS,p),q,r))
| ap_parcontractE_c2(comb_app(combS,p),q,r) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_84]),c_0_42]) ).
cnf(c_0_90,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),ap_parcontractE_sk2s(comb_app(combS,p),q,r)) != r
| ~ member(p,comb) ),
inference(spm,[status(thm)],[c_0_73,c_0_85]) ).
cnf(c_0_91,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_86,c_0_87]),c_0_88])]),c_0_80]),c_0_75]) ).
cnf(c_0_92,negated_conjecture,
( ap_parcontractE_sk2q(comb_app(combS,p),q,r) = comb_app(combS,p)
| comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(comb_app(combS,p),q,r) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_89]),c_0_34]) ).
cnf(c_0_93,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| comb_app(comb_app(combS,p),ap_parcontractE_sk2s(comb_app(combS,p),q,r)) != r ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
cnf(c_0_94,negated_conjecture,
( comb_app(comb_app(combS,p),q) != r
| ~ member(p,comb)
| ~ member(q,comb) ),
inference(spm,[status(thm)],[c_0_73,c_0_64]) ).
cnf(c_0_95,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| ap_parcontractE_c2(comb_app(combS,p),q,r) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_92]),c_0_42]),c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( comb_app(comb_app(combS,p),q) != r
| ~ member(q,comb) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_91])]) ).
cnf(c_0_97,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| comb_app(combK,r) = comb_app(combS,p) ),
inference(spm,[status(thm)],[c_0_50,c_0_95]) ).
cnf(c_0_98,negated_conjecture,
( comb_app(combK,r) = comb_app(combS,p)
| ~ member(q,comb) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_99,negated_conjecture,
( comb_app(comb_app(combS,p),ap_parcontractE_sk2s(X1,q,X2)) != r
| ~ ap_parcontractE_c4(X1,q,X2)
| ~ member(p,comb) ),
inference(spm,[status(thm)],[c_0_73,c_0_29]) ).
cnf(c_0_100,negated_conjecture,
( combK = X1
| comb_app(combS,p) != comb_app(X1,X2)
| ~ member(q,comb) ),
inference(spm,[status(thm)],[c_0_26,c_0_98]) ).
cnf(c_0_101,axiom,
combK != combS,
k_s ).
cnf(c_0_102,negated_conjecture,
( comb_app(comb_app(combS,p),X1) != r
| ~ ap_parcontractE_c4(X2,q,comb_app(X3,X1))
| ~ member(p,comb) ),
inference(spm,[status(thm)],[c_0_99,c_0_52]) ).
cnf(c_0_103,negated_conjecture,
( comb_app(comb_app(combS,p),q) = r
| member(q,comb) ),
inference(spm,[status(thm)],[c_0_53,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
~ member(q,comb),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_100]),c_0_101]) ).
cnf(c_0_105,negated_conjecture,
( comb_app(comb_app(combS,p),X1) != r
| ~ ap_parcontractE_c4(X2,q,comb_app(X3,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_91])]) ).
cnf(c_0_106,negated_conjecture,
comb_app(comb_app(combS,p),q) = r,
inference(sr,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,hypothesis,
( ap_parcontractE_c4(comb_app(combS,p),q,r)
| ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c1(comb_app(combS,p),q,r) ),
inference(sr,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_108,negated_conjecture,
~ ap_parcontractE_c4(X1,q,r),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_106])]) ).
cnf(c_0_109,hypothesis,
( ap_parcontractE_c2(comb_app(combS,p),q,r)
| ap_parcontractE_c1(comb_app(combS,p),q,r) ),
inference(sr,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_110,negated_conjecture,
~ member(r,comb),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_106]),c_0_104]) ).
cnf(c_0_111,hypothesis,
ap_parcontractE_c2(comb_app(combS,p),q,r),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_109]),c_0_106]),c_0_110]) ).
cnf(c_0_112,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_111]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL094-1 : TPTP v9.2.1. Released v2.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 16:16:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 15.29/9.59 % Version : CSE_E---1.7
% 15.29/9.59 % Problem : theBenchmark.p
% 15.29/9.59 % SZS status Unsatisfiable for theBenchmark.p
% 15.29/9.59 % SZS output start CNFRefutation
% See solution above
% 15.39/9.64 % Total time : 7.382s
%------------------------------------------------------------------------------