%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SEU306+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 : n016.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 17:52:07 EDT 2023

% Result   : Theorem 0.21s 0.47s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU306+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 23 22:43:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.47  Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.47  
% 0.21/0.47  % SZS status Theorem
% 0.21/0.47  
% 0.21/0.47  % SZS output start Proof
% 0.21/0.47  Take the following subset of the input axioms:
% 0.21/0.47    fof(d3_pre_topc, axiom, ![A2]: (one_sorted_str(A2) => cast_as_carrier_subset(A2)=the_carrier(A2))).
% 0.21/0.47    fof(t12_pre_topc, conjecture, ![A]: (one_sorted_str(A) => cast_as_carrier_subset(A)=the_carrier(A))).
% 0.21/0.47  
% 0.21/0.47  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.47  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.47  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.47    fresh(y, y, x1...xn) = u
% 0.21/0.47    C => fresh(s, t, x1...xn) = v
% 0.21/0.47  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.48  variables of u and v.
% 0.21/0.48  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.48  input problem has no model of domain size 1).
% 0.21/0.48  
% 0.21/0.48  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.48  
% 0.21/0.48  Axiom 1 (t12_pre_topc): one_sorted_str(a) = true2.
% 0.21/0.48  Axiom 2 (d3_pre_topc): fresh11(X, X, Y) = the_carrier(Y).
% 0.21/0.48  Axiom 3 (d3_pre_topc): fresh11(one_sorted_str(X), true2, X) = cast_as_carrier_subset(X).
% 0.21/0.48  
% 0.21/0.48  Goal 1 (t12_pre_topc_1): cast_as_carrier_subset(a) = the_carrier(a).
% 0.21/0.48  Proof:
% 0.21/0.48    cast_as_carrier_subset(a)
% 0.21/0.48  = { by axiom 3 (d3_pre_topc) R->L }
% 0.21/0.48    fresh11(one_sorted_str(a), true2, a)
% 0.21/0.48  = { by axiom 1 (t12_pre_topc) }
% 0.21/0.48    fresh11(true2, true2, a)
% 0.21/0.48  = { by axiom 2 (d3_pre_topc) }
% 0.21/0.48    the_carrier(a)
% 0.21/0.48  % SZS output end Proof
% 0.21/0.48  
% 0.21/0.48  RESULT: Theorem (the conjecture is true).
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