%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL001-2 : 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 : 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 04:11:57 PM UTC 2026
% Result : Unsatisfiable 0.30s 1.61s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of clauses : 46 ( 38 unt; 0 nHn; 20 RR)
% Number of literals : 56 ( 55 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 90 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sb_property,axiom,
apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i)) = apply(x,apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sb_property) ).
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(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(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(prove_fixed_point,negated_conjecture,
X1 != apply(combinator,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(i_definition,axiom,
apply(i,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).
cnf(i_0_6,axiom,
apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i)) = apply(x,apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))),
sb_property,
[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(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition,
[final] ).
cnf(i_0_9,axiom,
apply(apply(k,X1),X2) = X1,
k_definition,
[final] ).
cnf(i_0_10,negated_conjecture,
X1 != apply(combinator,X1),
prove_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_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,plain,
X1 = apply(i,X1),
inference(scs_inference,[],[i_0_11,i_0_13]) ).
cnf(i_0_18,plain,
X1 != apply(i,apply(combinator,X1)),
inference(scs_inference,[],[i_0_10,i_0_11,i_0_13,i_0_14]) ).
cnf(i_0_19,plain,
apply(i,X1) = X1,
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_20,plain,
X1 != apply(combinator,apply(i,X1)),
inference(scs_inference,[],[i_0_10,i_0_11,i_0_13,i_0_14,i_0_16]) ).
cnf(i_0_21,plain,
X1 = apply(apply(k,X1),X2),
inference(scs_inference,[],[i_0_9,i_0_13]) ).
cnf(i_0_22,plain,
X1 != apply(apply(k,apply(combinator,X1)),X2),
inference(scs_inference,[],[i_0_10,i_0_9,i_0_13,i_0_14]) ).
cnf(i_0_23,plain,
apply(apply(k,X1),X2) = X1,
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_24,plain,
X1 != apply(k,apply(combinator,apply(X1,X2))),
inference(scs_inference,[],[i_0_10,i_0_9,i_0_13,i_0_14,i_0_15]) ).
cnf(i_0_25,plain,
X1 != apply(combinator,apply(apply(k,X1),X2)),
inference(scs_inference,[],[i_0_10,i_0_9,i_0_13,i_0_14,i_0_15,i_0_16]) ).
cnf(i_0_26,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_27,plain,
X1 != apply(apply(apply(s,k),X2),apply(combinator,X1)),
inference(scs_inference,[],[i_0_22,i_0_7,i_0_13,i_0_14]) ).
cnf(i_0_28,plain,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_29,plain,
X1 != apply(apply(k,apply(combinator,X1)),X2),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_30,plain,
X1 != apply(combinator,apply(apply(apply(s,k),X2),X1)),
inference(scs_inference,[],[i_0_22,i_0_7,i_0_13,i_0_14,i_0_16]) ).
cnf(i_0_31,plain,
apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3),
inference(scs_inference,[],[i_0_8,i_0_13]) ).
cnf(i_0_32,plain,
apply(X1,X2) != apply(apply(apply(b,combinator),X1),X2),
inference(scs_inference,[],[i_0_10,i_0_8,i_0_13,i_0_14]) ).
cnf(i_0_33,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_34,plain,
X1 != apply(combinator,X1),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_35,plain,
X1 != apply(apply(b,combinator),X1),
inference(scs_inference,[],[i_0_10,i_0_8,i_0_13,i_0_14,i_0_15]) ).
cnf(i_0_36,plain,
apply(x,apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))) = apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i)),
inference(scs_inference,[],[i_0_6,i_0_13]) ).
cnf(i_0_37,plain,
apply(X1,apply(X2,X1)) != apply(apply(apply(s,apply(b,combinator)),X2),X1),
inference(scs_inference,[],[i_0_32,i_0_6,i_0_7,i_0_13,i_0_14]) ).
cnf(i_0_38,plain,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_39,plain,
apply(X1,X2) != apply(apply(apply(b,combinator),X1),X2),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_40,plain,
$false,
inference(scs_inference,[],[i_0_32,i_0_6,i_0_11,i_0_7,i_0_13,i_0_14,i_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL001-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 16:24:11 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.30/1.61 % Version : CSE_E---1.7
% 0.30/1.61 % Problem : theBenchmark.p
% 0.30/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.30/1.61 % SZS output start CNFRefutation
% See solution above
% 0.30/1.66 % Total time : 1.273s
%------------------------------------------------------------------------------