%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL090-1 : 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 : n027.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 04:12:18 PM UTC 2026
% Result : Unsatisfiable 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 44 ( 16 unt; 10 nHn; 44 RR)
% Number of literals : 87 ( 24 equ; 35 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 88 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
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_contractE12,axiom,
( X3 = comb_app(ap_contractE_sk2q(X1,X2,X3),X2)
| ~ ap_contractE_c3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE12) ).
cnf(k_contractE,axiom,
~ member(pair(combK,X1),contract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_contractE) ).
cnf(ap_contractE13,axiom,
( member(pair(X2,ap_contractE_sk3q(X1,X2,X3)),contract)
| ~ ap_contractE_c4(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE13) ).
cnf(ap_contractE1,axiom,
( ap_contractE_c1(X1,X2,X3)
| ap_contractE_c2(X1,X2,X3)
| ap_contractE_c3(X1,X2,X3)
| ap_contractE_c4(X1,X2,X3)
| ~ member(pair(comb_app(X1,X2),X3),contract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE1) ).
cnf(i_contract_E,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_contract_E) ).
cnf(ap_contractE10,axiom,
( member(pair(X1,ap_contractE_sk2q(X1,X2,X3)),contract)
| ~ ap_contractE_c3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE10) ).
cnf(s_contractE,axiom,
~ member(pair(combS,X1),contract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_contractE) ).
cnf(s_app,axiom,
combS != comb_app(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
cnf(ap_contractE9,axiom,
( X1 = comb_app(comb_app(combS,ap_contractE_sk1p(X1,X2,X3)),ap_contractE_sk1q(X1,X2,X3))
| ~ ap_contractE_c2(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE9) ).
cnf(ap_contractE4,axiom,
( X1 = comb_app(combK,X3)
| ~ ap_contractE_c1(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_contractE4) ).
cnf(k_s,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
cnf(c_0_12,axiom,
( X1 = X3
| comb_app(X1,X2) != comb_app(X3,X4) ),
app_app1 ).
cnf(c_0_13,axiom,
( X3 = comb_app(ap_contractE_sk2q(X1,X2,X3),X2)
| ~ ap_contractE_c3(X1,X2,X3) ),
ap_contractE12 ).
cnf(c_0_14,plain,
( ap_contractE_sk2q(X1,X2,comb_app(X3,X4)) = X3
| ~ ap_contractE_c3(X1,X2,comb_app(X3,X4)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_15,axiom,
~ member(pair(combK,X1),contract),
k_contractE ).
cnf(c_0_16,axiom,
( member(pair(X2,ap_contractE_sk3q(X1,X2,X3)),contract)
| ~ ap_contractE_c4(X1,X2,X3) ),
ap_contractE13 ).
cnf(c_0_17,plain,
( comb_app(X1,X2) = comb_app(X1,X3)
| ~ ap_contractE_c3(X4,X2,comb_app(X1,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
( ap_contractE_c1(X1,X2,X3)
| ap_contractE_c2(X1,X2,X3)
| ap_contractE_c3(X1,X2,X3)
| ap_contractE_c4(X1,X2,X3)
| ~ member(pair(comb_app(X1,X2),X3),contract) ),
ap_contractE1 ).
cnf(c_0_19,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
i_contract_E ).
cnf(c_0_20,plain,
~ ap_contractE_c4(X1,combK,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( comb_app(ap_contractE_sk2q(X1,X2,X3),X4) = X3
| ~ ap_contractE_c3(X5,X4,X3)
| ~ ap_contractE_c3(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,axiom,
( member(pair(X1,ap_contractE_sk2q(X1,X2,X3)),contract)
| ~ ap_contractE_c3(X1,X2,X3) ),
ap_contractE10 ).
cnf(c_0_24,negated_conjecture,
( comb_app(ap_contractE_sk2q(X1,X2,r),combK) = r
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ~ ap_contractE_c3(X1,X2,r) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( member(pair(X1,X2),contract)
| ~ ap_contractE_c3(X1,X3,comb_app(X2,X4)) ),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( comb_app(ap_contractE_sk2q(comb_app(combS,combK),combK,r),combK) = r
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| member(pair(X1,ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)
| ~ ap_contractE_c3(X1,X2,r) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,axiom,
~ member(pair(combS,X1),contract),
s_contractE ).
cnf(c_0_29,axiom,
combS != comb_app(X1,X2),
s_app ).
cnf(c_0_30,axiom,
( X1 = comb_app(comb_app(combS,ap_contractE_sk1p(X1,X2,X3)),ap_contractE_sk1q(X1,X2,X3))
| ~ ap_contractE_c2(X1,X2,X3) ),
ap_contractE9 ).
cnf(c_0_31,negated_conjecture,
( ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_32,plain,
~ ap_contractE_c3(combS,X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_33,plain,
~ ap_contractE_c2(combS,X1,X2),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_34,axiom,
( X1 = comb_app(combK,X3)
| ~ ap_contractE_c1(X1,X2,X3) ),
ap_contractE4 ).
cnf(c_0_35,negated_conjecture,
( ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_20]),c_0_32]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_29]) ).
cnf(c_0_37,plain,
( comb_app(combS,ap_contractE_sk1p(comb_app(X1,X2),X3,X4)) = X1
| ~ ap_contractE_c2(comb_app(X1,X2),X3,X4) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_30])]) ).
cnf(c_0_38,negated_conjecture,
( comb_app(combS,combK) = comb_app(combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_39,plain,
~ ap_contractE_c2(comb_app(combS,X1),X2,X3),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_37])]) ).
cnf(c_0_40,negated_conjecture,
comb_app(combS,combK) = comb_app(combK,r),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
( combS = X1
| comb_app(combK,r) != comb_app(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_40]) ).
cnf(c_0_42,axiom,
combK != combS,
k_s ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL090-1 : TPTP v9.2.1. Released v2.7.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 16:17:19 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------