%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL002-3 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 04:11:58 PM UTC 2026
% Result : Unsatisfiable 5.42s 5.63s
% Output : CNFRefutation 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of clauses : 75 ( 63 unt; 0 nHn; 11 RR)
% Number of literals : 91 ( 82 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 167 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_weak_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))),apply(s,apply(c,apply(b,X1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
cnf(c_definition,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(weak_fixed_point,axiom,
( fixed_point(X1)
| X1 != apply(fixed_pt,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
cnf(i_definition,axiom,
apply(i,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).
cnf(i_0_6,negated_conjecture,
~ fixed_point(apply(apply(apply(s,apply(c,apply(b,X1))),apply(s,apply(c,apply(b,X1)))),apply(s,apply(c,apply(b,X1))))),
prove_weak_fixed_point,
[final] ).
cnf(i_0_7,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition,
[final] ).
cnf(i_0_8,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
c_definition,
[final] ).
cnf(i_0_9,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition,
[final] ).
cnf(i_0_10,axiom,
( fixed_point(X1)
| X1 != apply(fixed_pt,X1) ),
weak_fixed_point,
[final] ).
cnf(i_0_11,axiom,
apply(i,X1) = X1,
i_definition,
[final] ).
cnf(i_0_12,axiom,
X1 = X1 ).
cnf(i_0_13,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_14,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_15,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_16,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_17,axiom,
( X1 != X2
| ~ fixed_point(X1)
| fixed_point(X2) ) ).
cnf(i_0_12_001,axiom,
X1 = X1 ).
cnf(i_0_13_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_14_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_15_004,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_16_005,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_17_006,axiom,
( X1 != X2
| ~ fixed_point(X1)
| fixed_point(X2) ) ).
cnf(i_0_18,plain,
X1 = apply(i,X1),
inference(scs_inference,[],[i_0_11,i_0_13]) ).
cnf(i_0_19,plain,
apply(apply(apply(b,i),X1),X2) = apply(X1,X2),
inference(scs_inference,[],[i_0_11,i_0_9,i_0_13,i_0_14]) ).
cnf(i_0_20,plain,
apply(i,X1) = X1,
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_21,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_22,plain,
apply(X1,X2) = apply(apply(apply(b,i),X1),X2),
inference(scs_inference,[],[i_0_19,i_0_13]) ).
cnf(i_0_23,plain,
apply(apply(apply(s,apply(b,i)),X1),X2) = apply(X2,apply(X1,X2)),
inference(scs_inference,[],[i_0_19,i_0_7,i_0_13,i_0_14]) ).
cnf(i_0_24,plain,
apply(apply(apply(b,i),X1),X2) = apply(X1,X2),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_25,plain,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_26,plain,
apply(X1,apply(X2,X1)) = apply(apply(apply(s,apply(b,i)),X2),X1),
inference(scs_inference,[],[i_0_23,i_0_13]) ).
cnf(i_0_27,plain,
apply(apply(apply(c,apply(s,apply(b,i))),X1),X2) = apply(X1,apply(X2,X1)),
inference(scs_inference,[],[i_0_23,i_0_8,i_0_13,i_0_14]) ).
cnf(i_0_28,plain,
apply(apply(apply(s,apply(b,i)),X1),X2) = apply(X2,apply(X1,X2)),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_29,plain,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_30,plain,
apply(X1,apply(X2,X1)) = apply(apply(apply(c,apply(s,apply(b,i))),X1),X2),
inference(scs_inference,[],[i_0_27,i_0_13]) ).
cnf(i_0_31,plain,
apply(X1,apply(X2,apply(apply(b,i),X1))) = apply(apply(apply(s,apply(b,i)),X2),apply(apply(b,i),X1)),
inference(scs_inference,[],[i_0_26,i_0_22,i_0_27,i_0_13,i_0_14]) ).
cnf(i_0_32,plain,
apply(X1,apply(X2,X1)) = apply(apply(apply(s,apply(b,i)),X2),X1),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_33,plain,
apply(X1,X2) = apply(apply(apply(b,i),X1),X2),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_34,plain,
apply(apply(apply(s,apply(b,i)),X1),apply(apply(b,i),X2)) = apply(X2,apply(X1,apply(apply(b,i),X2))),
inference(scs_inference,[],[i_0_31,i_0_13]) ).
cnf(i_0_35,plain,
apply(X1,apply(X2,X1)) = apply(apply(apply(b,i),apply(apply(c,apply(s,apply(b,i))),X1)),X2),
inference(scs_inference,[],[i_0_30,i_0_31,i_0_22,i_0_13,i_0_14]) ).
cnf(i_0_36,plain,
apply(X1,X2) = apply(apply(apply(b,i),X1),X2),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_37,plain,
apply(apply(apply(b,i),apply(apply(c,apply(s,apply(b,i))),X1)),X2) = apply(X1,apply(X2,X1)),
inference(scs_inference,[],[i_0_35,i_0_13]) ).
cnf(i_0_38,plain,
apply(X1,i) = apply(apply(apply(b,i),apply(apply(c,apply(s,apply(b,i))),i)),X1),
inference(scs_inference,[],[i_0_35,i_0_18,i_0_13,i_0_14]) ).
cnf(i_0_39,plain,
apply(X1,apply(X2,X1)) = apply(apply(apply(b,i),apply(apply(c,apply(s,apply(b,i))),X1)),X2),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_40,plain,
X1 = apply(i,X1),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_41,plain,
apply(apply(apply(b,i),apply(apply(c,apply(s,apply(b,i))),i)),X1) = apply(X1,i),
inference(scs_inference,[],[i_0_38,i_0_13]) ).
cnf(i_0_42,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(scs_inference,[],[i_0_7,i_0_13]) ).
cnf(i_0_43,plain,
apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2),
inference(scs_inference,[],[i_0_8,i_0_13]) ).
cnf(i_0_44,plain,
apply(apply(apply(b,i),apply(apply(b,i),X1)),apply(X2,apply(apply(b,i),X1))) = apply(X1,apply(X2,apply(apply(b,i),X1))),
inference(scs_inference,[],[i_0_42,i_0_34,i_0_8,i_0_13,i_0_14]) ).
cnf(i_0_45,plain,
apply(apply(apply(s,apply(b,i)),X1),apply(apply(b,i),X2)) = apply(X2,apply(X1,apply(apply(b,i),X2))),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_46,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_47,plain,
apply(X1,apply(X2,apply(apply(b,i),X1))) = apply(apply(apply(b,i),apply(apply(b,i),X1)),apply(X2,apply(apply(b,i),X1))),
inference(scs_inference,[],[i_0_44,i_0_13]) ).
cnf(i_0_48,plain,
apply(apply(X1,apply(X2,apply(apply(c,X1),X3))),X3) = apply(apply(apply(s,apply(b,i)),X2),apply(apply(c,X1),X3)),
inference(scs_inference,[],[i_0_43,i_0_44,i_0_26,i_0_13,i_0_14]) ).
cnf(i_0_49,plain,
apply(X1,apply(X2,X1)) = apply(apply(apply(s,apply(b,i)),X2),X1),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_50,plain,
apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_51,plain,
apply(apply(apply(s,apply(b,i)),X1),apply(apply(c,X2),X3)) = apply(apply(X2,apply(X1,apply(apply(c,X2),X3))),X3),
inference(scs_inference,[],[i_0_48,i_0_13]) ).
cnf(i_0_52,plain,
apply(apply(X1,apply(X2,apply(apply(c,X1),X2))),X2) = apply(apply(apply(s,apply(s,apply(b,i))),apply(c,X1)),X2),
inference(scs_inference,[],[i_0_48,i_0_42,i_0_13,i_0_14]) ).
cnf(i_0_53,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_54,plain,
apply(apply(X1,apply(X2,apply(apply(c,X1),X3))),X3) = apply(apply(apply(s,apply(b,i)),X2),apply(apply(c,X1),X3)),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_55,plain,
apply(apply(apply(s,apply(s,apply(b,i))),apply(c,X1)),X2) = apply(apply(X1,apply(X2,apply(apply(c,X1),X2))),X2),
inference(scs_inference,[],[i_0_52,i_0_13]) ).
cnf(i_0_56,plain,
apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3),
inference(scs_inference,[],[i_0_9,i_0_13]) ).
cnf(i_0_57,plain,
apply(X1,apply(X2,X3)) = apply(apply(apply(c,apply(b,X1)),X3),X2),
inference(scs_inference,[],[i_0_56,i_0_43,i_0_14]) ).
cnf(i_0_58,plain,
apply(apply(X1,X2),X3) = apply(apply(apply(c,X1),X3),X2),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_59,plain,
apply(apply(apply(c,apply(b,X1)),X2),X3) = apply(X1,apply(X3,X2)),
inference(scs_inference,[],[i_0_56,i_0_43,i_0_14,i_0_13]) ).
cnf(i_0_60,plain,
apply(apply(apply(c,apply(b,X1)),apply(apply(b,i),X1)),X2) = apply(apply(apply(b,i),apply(apply(b,i),X1)),apply(X2,apply(apply(b,i),X1))),
inference(scs_inference,[],[i_0_59,i_0_47,i_0_14]) ).
cnf(i_0_61,plain,
apply(X1,apply(X2,apply(apply(b,i),X1))) = apply(apply(apply(b,i),apply(apply(b,i),X1)),apply(X2,apply(apply(b,i),X1))),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_62,plain,
apply(apply(apply(c,apply(b,X1)),X2),X3) = apply(X1,apply(X3,X2)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_63,plain,
apply(apply(apply(b,i),apply(apply(b,i),X1)),apply(X2,apply(apply(b,i),X1))) = apply(apply(apply(c,apply(b,X1)),apply(apply(b,i),X1)),X2),
inference(scs_inference,[],[i_0_59,i_0_47,i_0_14,i_0_13]) ).
cnf(i_0_64,plain,
apply(X1,apply(apply(X2,X3),X3)) = apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3),
inference(scs_inference,[],[i_0_57,i_0_42,i_0_14]) ).
cnf(i_0_65,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_66,plain,
apply(X1,apply(X2,X3)) = apply(apply(apply(c,apply(b,X1)),X3),X2),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_67,plain,
apply(apply(apply(s,apply(c,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X3)),
inference(scs_inference,[],[i_0_57,i_0_42,i_0_14,i_0_13]) ).
cnf(i_0_68,plain,
$false,
inference(scs_inference,[],[i_0_6,i_0_57,i_0_42,i_0_14,i_0_13,i_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL002-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 16:14:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 5.42/5.63 % Version : CSE_E---1.7
% 5.42/5.63 % Problem : theBenchmark.p
% 5.42/5.63 % SZS status Unsatisfiable for theBenchmark.p
% 5.42/5.63 % SZS output start CNFRefutation
% See solution above
% 5.61/5.71 % Total time : 5.281s
%------------------------------------------------------------------------------