%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN551+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% 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 : n031.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 05:39:27 PM UTC 2026
% Result : Theorem 4.82s 3.53s
% Output : CNFRefutation 4.82s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
( ( ? [X1] : X1 = f(g(X1))
& ! [X2,X3] :
( ( X2 = f(g(X2))
& X3 = f(g(X3)) )
=> X2 = X3 ) )
<=> ( ? [X1] : X1 = g(f(X1))
& ! [X2,X3] :
( ( X2 = g(f(X2))
& X3 = g(f(X3)) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_cute_thing) ).
fof(c_0_1,negated_conjecture,
~ ( ( ? [X1] : X1 = f(g(X1))
& ! [X2,X3] :
( ( X2 = f(g(X2))
& X3 = f(g(X3)) )
=> X2 = X3 ) )
<=> ( ? [X1] : X1 = g(f(X1))
& ! [X2,X3] :
( ( X2 = g(f(X2))
& X3 = g(f(X3)) )
=> X2 = X3 ) ) ),
inference(assume_negation,[status(cth)],[prove_this_cute_thing]) ).
fof(c_0_2,negated_conjecture,
! [X10,X13,X17,X18,X20,X21] :
( ( esk3_0 = g(f(esk3_0))
| X13 != g(f(X13))
| esk1_0 = f(g(esk1_0))
| X10 != f(g(X10)) )
& ( esk4_0 = g(f(esk4_0))
| X13 != g(f(X13))
| esk1_0 = f(g(esk1_0))
| X10 != f(g(X10)) )
& ( esk3_0 != esk4_0
| X13 != g(f(X13))
| esk1_0 = f(g(esk1_0))
| X10 != f(g(X10)) )
& ( esk3_0 = g(f(esk3_0))
| X13 != g(f(X13))
| esk2_0 = f(g(esk2_0))
| X10 != f(g(X10)) )
& ( esk4_0 = g(f(esk4_0))
| X13 != g(f(X13))
| esk2_0 = f(g(esk2_0))
| X10 != f(g(X10)) )
& ( esk3_0 != esk4_0
| X13 != g(f(X13))
| esk2_0 = f(g(esk2_0))
| X10 != f(g(X10)) )
& ( esk3_0 = g(f(esk3_0))
| X13 != g(f(X13))
| esk1_0 != esk2_0
| X10 != f(g(X10)) )
& ( esk4_0 = g(f(esk4_0))
| X13 != g(f(X13))
| esk1_0 != esk2_0
| X10 != f(g(X10)) )
& ( esk3_0 != esk4_0
| X13 != g(f(X13))
| esk1_0 != esk2_0
| X10 != f(g(X10)) )
& ( esk6_0 = g(f(esk6_0))
| esk5_0 = f(g(esk5_0)) )
& ( X20 != g(f(X20))
| X21 != g(f(X21))
| X20 = X21
| esk5_0 = f(g(esk5_0)) )
& ( esk6_0 = g(f(esk6_0))
| X17 != f(g(X17))
| X18 != f(g(X18))
| X17 = X18 )
& ( X20 != g(f(X20))
| X21 != g(f(X21))
| X20 = X21
| X17 != f(g(X17))
| X18 != f(g(X18))
| X17 = X18 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( esk3_0 = g(f(esk3_0))
| esk1_0 = f(g(esk1_0))
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( esk6_0 = g(f(esk6_0))
| esk5_0 = f(g(esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| g(f(esk3_0)) = esk3_0
| f(g(esk1_0)) = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,negated_conjecture,
( esk3_0 = g(f(esk3_0))
| esk2_0 = f(g(esk2_0))
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
( esk4_0 = g(f(esk4_0))
| esk1_0 = f(g(esk1_0))
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
( esk6_0 = g(f(esk6_0))
| X1 = X2
| X1 != f(g(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| g(f(esk3_0)) = esk3_0
| g(f(esk6_0)) = esk6_0 ),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| g(f(esk3_0)) = esk3_0
| f(g(esk2_0)) = esk2_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| g(f(esk4_0)) = esk4_0
| f(g(esk1_0)) = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_12,negated_conjecture,
( esk4_0 = g(f(esk4_0))
| esk2_0 = f(g(esk2_0))
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| g(f(esk6_0)) = esk6_0
| X1 = esk1_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| g(f(esk3_0)) = esk3_0
| g(f(esk6_0)) = esk6_0 ),
inference(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_15,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| g(f(esk4_0)) = esk4_0
| g(f(esk6_0)) = esk6_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| g(f(esk4_0)) = esk4_0
| f(g(esk2_0)) = esk2_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| g(f(esk3_0)) = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| g(f(esk6_0)) = esk6_0
| X1 = esk1_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| g(f(esk4_0)) = esk4_0
| g(f(esk6_0)) = esk6_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_4]) ).
cnf(c_0_20,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| f(g(esk1_0)) = esk1_0
| esk2_0 = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_3,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| g(f(esk4_0)) = esk4_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( X1 = X2
| X3 = X4
| X1 != g(f(X1))
| X2 != g(f(X2))
| X3 != f(g(X3))
| X4 != f(g(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_23,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| g(f(esk3_0)) = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( esk3_0 = g(f(esk3_0))
| X1 != g(f(X1))
| esk1_0 != esk2_0
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_25,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| f(g(esk2_0)) = esk2_0
| esk2_0 = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| f(g(esk1_0)) = esk1_0
| esk2_0 = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| X1 = esk1_0
| X2 = X3
| f(g(X1)) != X1
| g(f(X3)) != X3
| g(f(X2)) != X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| g(f(esk3_0)) = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| g(f(esk4_0)) = esk4_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( esk4_0 = g(f(esk4_0))
| X1 != g(f(X1))
| esk1_0 != esk2_0
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_31,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| f(g(esk2_0)) = esk2_0
| esk2_0 = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| esk2_0 = esk1_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| X1 = esk1_0
| X2 = X3
| f(g(X1)) != X1
| g(f(X3)) != X3
| g(f(X2)) != X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| g(f(esk4_0)) = esk4_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| X1 = g(esk2_0)
| esk2_0 = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk2_0 = esk1_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( g(esk2_0) = g(esk1_0)
| g(f(esk3_0)) = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_38,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| X1 = g(esk2_0)
| esk2_0 = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( g(esk2_0) = g(esk1_0)
| X1 = f(esk3_0)
| esk2_0 = esk1_0
| X2 = X3
| f(g(X1)) != X1
| g(f(X3)) != X3
| g(f(X2)) != X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( g(esk2_0) = g(esk1_0)
| g(f(esk4_0)) = esk4_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_41,negated_conjecture,
( f(esk4_0) = f(esk3_0)
| g(esk2_0) = g(esk1_0)
| esk2_0 = esk1_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( g(esk2_0) = g(esk1_0)
| f(esk4_0) = f(esk3_0)
| esk2_0 = esk1_0
| X1 = esk4_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( f(esk4_0) = f(esk3_0)
| g(esk2_0) = g(esk1_0)
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( g(f(esk3_0)) = esk4_0
| g(esk2_0) = g(esk1_0)
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_40,c_0_43]) ).
cnf(c_0_45,negated_conjecture,
( g(esk2_0) = g(esk1_0)
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_46,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| f(g(esk1_0)) = esk2_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
( X1 = X2
| esk5_0 = f(g(esk5_0))
| X1 != g(f(X1))
| X2 != g(f(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_48,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| f(g(esk1_0)) = esk2_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( f(g(esk5_0)) = esk5_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0
| X1 = esk3_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( f(g(esk5_0)) = esk5_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
( esk2_0 = esk1_0
| esk4_0 = esk3_0
| X1 = esk5_0
| X2 = X3
| f(g(X1)) != X1
| g(f(X3)) != X3
| g(f(X2)) != X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| X1 = esk5_0
| f(g(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_8,c_0_4]) ).
cnf(c_0_55,negated_conjecture,
( f(esk4_0) = esk5_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_53,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| f(esk4_0) = esk5_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( f(esk4_0) = esk5_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0
| X1 = esk6_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_58,negated_conjecture,
( f(esk3_0) = esk5_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_53,c_0_48]) ).
cnf(c_0_59,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| f(esk3_0) = esk5_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
cnf(c_0_60,negated_conjecture,
( g(esk5_0) = esk6_0
| f(esk4_0) = esk5_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_57,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( f(esk4_0) = esk5_0
| esk6_0 = esk4_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_57,c_0_51]) ).
cnf(c_0_62,negated_conjecture,
( f(esk3_0) = esk5_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0
| X1 = esk6_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( g(esk5_0) = esk6_0
| g(esk5_0) = esk4_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_51,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( g(esk5_0) = esk4_0
| esk6_0 = esk4_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_51,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( f(esk3_0) = esk5_0
| esk6_0 = esk4_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_51]) ).
cnf(c_0_66,negated_conjecture,
( f(esk3_0) = esk5_0
| esk6_0 = esk3_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_48]) ).
cnf(c_0_67,negated_conjecture,
( g(esk5_0) = esk4_0
| esk4_0 = esk3_0
| esk2_0 = esk1_0 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_63]),c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( g(esk5_0) = esk3_0
| esk6_0 = esk4_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_48,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
( g(esk5_0) = esk3_0
| esk6_0 = esk3_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_48,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
( esk6_0 = esk4_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( esk6_0 = esk3_0
| esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( esk2_0 = esk1_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_73,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| esk4_0 = esk3_0
| f(g(X1)) != X1
| g(f(X2)) != X2 ),
inference(spm,[status(thm)],[c_0_24,c_0_72]) ).
cnf(c_0_74,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| g(f(esk3_0)) = esk3_0
| esk4_0 = esk3_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_73,c_0_4]) ).
cnf(c_0_75,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| g(f(esk6_0)) = esk6_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_74,c_0_4]) ).
cnf(c_0_76,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| esk4_0 = esk3_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_73,c_0_75]) ).
cnf(c_0_77,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk4_0 = esk3_0
| f(g(X1)) != X1
| g(f(X2)) != X2 ),
inference(spm,[status(thm)],[c_0_30,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( g(f(esk3_0)) = esk3_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_76,c_0_75]) ).
cnf(c_0_79,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk4_0 = esk3_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_80,negated_conjecture,
( f(g(esk5_0)) = esk5_0
| esk4_0 = esk3_0
| X1 = esk3_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_47,c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( g(f(esk4_0)) = esk4_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_79,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( f(g(esk5_0)) = esk5_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_83,negated_conjecture,
( esk4_0 = esk3_0
| X1 = esk5_0
| X2 = X3
| f(g(X1)) != X1
| g(f(X3)) != X3
| g(f(X2)) != X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_82]) ).
cnf(c_0_84,negated_conjecture,
( f(esk4_0) = esk5_0
| esk4_0 = esk3_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_83,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| f(esk4_0) = esk5_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( f(esk4_0) = esk5_0
| esk4_0 = esk3_0
| X1 = esk6_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_87,negated_conjecture,
( f(esk3_0) = esk5_0
| esk4_0 = esk3_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_83,c_0_78]) ).
cnf(c_0_88,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| f(esk3_0) = esk5_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_78]) ).
cnf(c_0_89,negated_conjecture,
( g(esk5_0) = esk6_0
| f(esk4_0) = esk5_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_86,c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( f(esk4_0) = esk5_0
| esk6_0 = esk4_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_86,c_0_81]) ).
cnf(c_0_91,negated_conjecture,
( f(esk3_0) = esk5_0
| esk4_0 = esk3_0
| X1 = esk6_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( g(esk5_0) = esk6_0
| g(esk5_0) = esk4_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_81,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
( g(esk5_0) = esk4_0
| esk6_0 = esk4_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_81,c_0_90]) ).
cnf(c_0_94,negated_conjecture,
( f(esk3_0) = esk5_0
| esk6_0 = esk4_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_91,c_0_81]) ).
cnf(c_0_95,negated_conjecture,
( f(esk3_0) = esk5_0
| esk6_0 = esk3_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_91,c_0_78]) ).
cnf(c_0_96,negated_conjecture,
( g(esk5_0) = esk4_0
| esk4_0 = esk3_0 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_92]),c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( g(esk5_0) = esk3_0
| esk6_0 = esk4_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_78,c_0_94]) ).
cnf(c_0_98,negated_conjecture,
( g(esk5_0) = esk3_0
| esk6_0 = esk3_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_78,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( esk6_0 = esk4_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,negated_conjecture,
( esk6_0 = esk3_0
| esk4_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_96,c_0_98]) ).
cnf(c_0_101,negated_conjecture,
( esk2_0 = f(g(esk2_0))
| esk3_0 != esk4_0
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_102,negated_conjecture,
esk4_0 = esk3_0,
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_103,negated_conjecture,
( esk1_0 = f(g(esk1_0))
| esk3_0 != esk4_0
| X1 != g(f(X1))
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_104,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| f(g(X1)) != X1
| g(f(X2)) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
cnf(c_0_105,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| f(g(X1)) != X1
| g(f(X2)) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_102])]) ).
cnf(c_0_106,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| f(g(esk2_0)) = esk2_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_104,c_0_4]) ).
cnf(c_0_107,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| f(g(esk1_0)) = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_105,c_0_4]) ).
cnf(c_0_108,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| g(f(esk6_0)) = esk6_0 ),
inference(spm,[status(thm)],[c_0_106,c_0_4]) ).
cnf(c_0_109,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| g(f(esk6_0)) = esk6_0 ),
inference(spm,[status(thm)],[c_0_107,c_0_4]) ).
cnf(c_0_110,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| esk5_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_108]) ).
cnf(c_0_111,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| esk5_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_109]) ).
cnf(c_0_112,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| esk5_0 = esk2_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_104,c_0_110]) ).
cnf(c_0_113,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| esk5_0 = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_104,c_0_111]) ).
cnf(c_0_114,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| esk5_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_112,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| esk5_0 = esk2_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_105,c_0_110]) ).
cnf(c_0_116,negated_conjecture,
( f(g(esk2_0)) = esk2_0
| esk5_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_113,c_0_111]) ).
cnf(c_0_117,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| esk5_0 = esk1_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_105,c_0_111]) ).
cnf(c_0_118,negated_conjecture,
( esk5_0 = esk2_0
| X1 = esk2_0
| X2 = X3
| f(g(X1)) != X1
| g(f(X3)) != X3
| g(f(X2)) != X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_114]) ).
cnf(c_0_119,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| esk5_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_115,c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( esk5_0 = esk1_0
| X1 = esk2_0
| X2 = X3
| f(g(X1)) != X1
| g(f(X3)) != X3
| g(f(X2)) != X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
( f(g(esk1_0)) = esk1_0
| esk5_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_117,c_0_116]) ).
cnf(c_0_122,negated_conjecture,
( esk2_0 = esk1_0
| esk5_0 = esk2_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( esk2_0 = esk1_0
| esk5_0 = esk1_0
| X1 = X2
| g(f(X2)) != X2
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_124,negated_conjecture,
( esk5_0 = esk2_0
| esk2_0 = esk1_0
| X1 = esk6_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_122,c_0_110]) ).
cnf(c_0_125,negated_conjecture,
( esk5_0 = esk1_0
| esk2_0 = esk1_0
| X1 = esk6_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_123,c_0_111]) ).
cnf(c_0_126,negated_conjecture,
( g(esk2_0) = esk6_0
| esk2_0 = esk1_0
| esk5_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_124,c_0_114]) ).
cnf(c_0_127,negated_conjecture,
( g(esk1_0) = esk6_0
| esk2_0 = esk1_0
| esk5_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_124,c_0_119]) ).
cnf(c_0_128,negated_conjecture,
( g(esk2_0) = esk6_0
| esk2_0 = esk1_0
| esk5_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_125,c_0_116]) ).
cnf(c_0_129,negated_conjecture,
( g(esk1_0) = esk6_0
| esk2_0 = esk1_0
| esk5_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_125,c_0_121]) ).
cnf(c_0_130,negated_conjecture,
( f(esk6_0) = esk2_0
| esk2_0 = esk1_0
| esk5_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_114,c_0_126]) ).
cnf(c_0_131,negated_conjecture,
( f(esk6_0) = esk1_0
| esk2_0 = esk1_0
| esk5_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_119,c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( f(esk6_0) = esk2_0
| esk2_0 = esk1_0
| esk5_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_116,c_0_128]) ).
cnf(c_0_133,negated_conjecture,
( f(esk6_0) = esk1_0
| esk2_0 = esk1_0
| esk5_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_121,c_0_129]) ).
cnf(c_0_134,negated_conjecture,
( esk3_0 != esk4_0
| X1 != g(f(X1))
| esk1_0 != esk2_0
| X2 != f(g(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_135,negated_conjecture,
( esk5_0 = esk2_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_136,negated_conjecture,
( esk5_0 = esk1_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( f(g(X1)) != X1
| g(f(X2)) != X2
| esk2_0 != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_102])]) ).
cnf(c_0_138,negated_conjecture,
esk2_0 = esk1_0,
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_139,negated_conjecture,
( f(g(X1)) != X1
| g(f(X2)) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138])]) ).
cnf(c_0_140,negated_conjecture,
( g(f(esk6_0)) = esk6_0
| g(f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_139,c_0_109]) ).
cnf(c_0_141,negated_conjecture,
g(f(esk6_0)) = esk6_0,
inference(spm,[status(thm)],[c_0_140,c_0_109]) ).
cnf(c_0_142,negated_conjecture,
g(f(X1)) != X1,
inference(spm,[status(thm)],[c_0_139,c_0_141]) ).
cnf(c_0_143,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_141,c_0_142]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN551+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% 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
% 0.14/0.32 % Computer : n031.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 : Tue May 5 08:41:54 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 4.82/3.53 % Version : CSE_E---1.7
% 4.82/3.53 % Problem : theBenchmark.p
% 4.82/3.53 % SZS status Theorem for theBenchmark.p
% 4.82/3.53 % SZS output start CNFRefutation
% See solution above
% 4.82/3.55 % Total time : 2.370s
%------------------------------------------------------------------------------