%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SEU150+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% 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 : Thu Aug 31 17:51:13 EDT 2023

% Result   : Theorem 0.19s 0.38s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU150+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n031.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 16:46:05 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.38  Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.38  
% 0.19/0.38  % SZS status Theorem
% 0.19/0.38  
% 0.19/0.38  % SZS output start Proof
% 0.19/0.38  Take the following subset of the input axioms:
% 0.19/0.38    fof(commutativity_k2_tarski, axiom, ![A, B]: unordered_pair(A, B)=unordered_pair(B, A)).
% 0.19/0.38    fof(t8_zfmisc_1, axiom, ![C, A2, B2]: (singleton(A2)=unordered_pair(B2, C) => A2=B2)).
% 0.19/0.38    fof(t9_zfmisc_1, conjecture, ![A3, B2, C2]: (singleton(A3)=unordered_pair(B2, C2) => B2=C2)).
% 0.19/0.38  
% 0.19/0.38  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.38  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.38  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.38    fresh(y, y, x1...xn) = u
% 0.19/0.38    C => fresh(s, t, x1...xn) = v
% 0.19/0.38  where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.38  variables of u and v.
% 0.19/0.38  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.38  input problem has no model of domain size 1).
% 0.19/0.38  
% 0.19/0.38  The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.38  
% 0.19/0.38  Axiom 1 (commutativity_k2_tarski): unordered_pair(X, Y) = unordered_pair(Y, X).
% 0.19/0.38  Axiom 2 (t9_zfmisc_1): singleton(a) = unordered_pair(b, c).
% 0.19/0.38  Axiom 3 (t8_zfmisc_1): fresh(X, X, Y, Z) = Z.
% 0.19/0.38  Axiom 4 (t8_zfmisc_1): fresh(singleton(X), unordered_pair(Y, Z), X, Y) = X.
% 0.19/0.38  
% 0.19/0.38  Goal 1 (t9_zfmisc_1_1): b = c.
% 0.19/0.38  Proof:
% 0.19/0.38    b
% 0.19/0.38  = { by axiom 4 (t8_zfmisc_1) R->L }
% 0.19/0.38    fresh(singleton(b), unordered_pair(c, b), b, c)
% 0.19/0.38  = { by axiom 1 (commutativity_k2_tarski) }
% 0.19/0.38    fresh(singleton(b), unordered_pair(b, c), b, c)
% 0.19/0.38  = { by axiom 2 (t9_zfmisc_1) R->L }
% 0.19/0.38    fresh(singleton(b), singleton(a), b, c)
% 0.19/0.38  = { by axiom 4 (t8_zfmisc_1) R->L }
% 0.19/0.39    fresh(singleton(b), singleton(fresh(singleton(a), unordered_pair(b, c), a, b)), b, c)
% 0.19/0.39  = { by axiom 2 (t9_zfmisc_1) R->L }
% 0.19/0.39    fresh(singleton(b), singleton(fresh(singleton(a), singleton(a), a, b)), b, c)
% 0.19/0.39  = { by axiom 3 (t8_zfmisc_1) }
% 0.19/0.39    fresh(singleton(b), singleton(b), b, c)
% 0.19/0.39  = { by axiom 3 (t8_zfmisc_1) }
% 0.19/0.39    c
% 0.19/0.39  % SZS output end Proof
% 0.19/0.39  
% 0.19/0.39  RESULT: Theorem (the conjecture is true).
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