TSTP Solution File: ALG240-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG240-1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n007.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 : Wed Aug 30 16:42:42 EDT 2023
% Result : Unsatisfiable 10.37s 2.63s
% Output : Proof 11.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.18 % Problem : ALG240-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.19 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.39 % Computer : n007.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8042.1875MB
% 0.09/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Mon Aug 28 05:36:27 EDT 2023
% 0.09/0.39 % CPUTime :
% 10.37/2.63 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 10.37/2.63
% 10.37/2.63 % SZS status Unsatisfiable
% 10.37/2.64
% 11.12/2.74 % SZS output start Proof
% 11.12/2.74 Axiom 1 (c01): mult(X, mult(Y, Z)) = mult(mult(X, Y), mult(X, Z)).
% 11.12/2.74 Axiom 2 (c02): mult(mult(X, Y), Z) = mult(mult(X, Z), mult(Y, Z)).
% 11.12/2.74 Axiom 3 (c03): mult(mult(mult(X, Y), mult(Z, W)), mult(mult(mult(X, Y), mult(Z, W)), mult(mult(X, Z), mult(Y, W)))) = mult(mult(X, Z), mult(Y, W)).
% 11.12/2.74 Axiom 4 (c04): mult(mult(mult(mult(X, Y), mult(Z, W)), mult(mult(X, Z), mult(Y, W))), mult(mult(X, Z), mult(Y, W))) = mult(mult(X, Y), mult(Z, W)).
% 11.12/2.74
% 11.12/2.74 Lemma 5: mult(mult(X, X), Y) = mult(X, mult(Y, Y)).
% 11.12/2.74 Proof:
% 11.12/2.74 mult(mult(X, X), Y)
% 11.12/2.74 = { by axiom 2 (c02) }
% 11.12/2.74 mult(mult(X, Y), mult(X, Y))
% 11.12/2.74 = { by axiom 1 (c01) R->L }
% 11.12/2.74 mult(X, mult(Y, Y))
% 11.12/2.74
% 11.12/2.74 Lemma 6: mult(mult(mult(X, Y), mult(X, Y)), mult(Z, W)) = mult(mult(X, Y), mult(Z, W)).
% 11.12/2.74 Proof:
% 11.12/2.74 mult(mult(mult(X, Y), mult(X, Y)), mult(Z, W))
% 11.12/2.74 = { by lemma 5 }
% 11.12/2.74 mult(mult(X, Y), mult(mult(Z, W), mult(Z, W)))
% 11.12/2.74 = { by axiom 4 (c04) R->L }
% 11.12/2.74 mult(mult(mult(mult(X, Y), mult(mult(Z, W), mult(Z, W))), mult(mult(X, mult(Z, W)), mult(Y, mult(Z, W)))), mult(mult(X, mult(Z, W)), mult(Y, mult(Z, W))))
% 11.12/2.74 = { by axiom 2 (c02) R->L }
% 11.12/2.74 mult(mult(mult(mult(X, Y), mult(mult(Z, W), mult(Z, W))), mult(mult(X, Y), mult(Z, W))), mult(mult(X, mult(Z, W)), mult(Y, mult(Z, W))))
% 11.12/2.74 = { by axiom 2 (c02) R->L }
% 11.12/2.74 mult(mult(mult(mult(X, Y), mult(mult(Z, W), mult(Z, W))), mult(mult(X, Y), mult(Z, W))), mult(mult(X, Y), mult(Z, W)))
% 11.12/2.74 = { by axiom 1 (c01) R->L }
% 11.12/2.74 mult(mult(mult(X, Y), mult(mult(mult(Z, W), mult(Z, W)), mult(Z, W))), mult(mult(X, Y), mult(Z, W)))
% 11.12/2.74 = { by axiom 1 (c01) R->L }
% 11.12/2.74 mult(mult(X, Y), mult(mult(mult(mult(Z, W), mult(Z, W)), mult(Z, W)), mult(Z, W)))
% 11.12/2.74 = { by axiom 2 (c02) }
% 11.12/2.74 mult(mult(X, Y), mult(mult(mult(mult(Z, W), mult(Z, W)), mult(Z, W)), mult(mult(Z, W), mult(Z, W))))
% 11.12/2.74 = { by lemma 5 }
% 11.12/2.74 mult(mult(X, Y), mult(mult(mult(Z, W), mult(mult(Z, W), mult(Z, W))), mult(mult(Z, W), mult(Z, W))))
% 11.12/2.74 = { by axiom 1 (c01) }
% 11.12/2.74 mult(mult(mult(X, Y), mult(mult(Z, W), mult(mult(Z, W), mult(Z, W)))), mult(mult(X, Y), mult(mult(Z, W), mult(Z, W))))
% 11.12/2.74 = { by lemma 5 R->L }
% 11.12/2.74 mult(mult(mult(X, Y), mult(mult(Z, W), mult(mult(Z, W), mult(Z, W)))), mult(mult(mult(X, Y), mult(X, Y)), mult(Z, W)))
% 11.12/2.74 = { by axiom 1 (c01) }
% 11.12/2.74 mult(mult(mult(mult(X, Y), mult(Z, W)), mult(mult(X, Y), mult(mult(Z, W), mult(Z, W)))), mult(mult(mult(X, Y), mult(X, Y)), mult(Z, W)))
% 11.12/2.74 = { by axiom 1 (c01) }
% 11.12/2.74 mult(mult(mult(mult(mult(X, Y), Z), mult(mult(X, Y), W)), mult(mult(X, Y), mult(mult(Z, W), mult(Z, W)))), mult(mult(mult(X, Y), mult(X, Y)), mult(Z, W)))
% 11.12/2.74 = { by lemma 5 R->L }
% 11.12/2.74 mult(mult(mult(mult(mult(X, Y), Z), mult(mult(X, Y), W)), mult(mult(mult(X, Y), mult(X, Y)), mult(Z, W))), mult(mult(mult(X, Y), mult(X, Y)), mult(Z, W)))
% 11.12/2.74 = { by axiom 4 (c04) }
% 11.12/2.74 mult(mult(mult(X, Y), Z), mult(mult(X, Y), W))
% 11.12/2.74 = { by axiom 1 (c01) R->L }
% 11.12/2.74 mult(mult(X, Y), mult(Z, W))
% 11.12/2.74
% 11.12/2.74 Lemma 7: mult(mult(mult(mult(X, Y), Z), mult(mult(X, Y), mult(Z, Z))), mult(mult(X, Y), mult(Z, Z))) = mult(mult(X, Y), Z).
% 11.12/2.74 Proof:
% 11.12/2.74 mult(mult(mult(mult(X, Y), Z), mult(mult(X, Y), mult(Z, Z))), mult(mult(X, Y), mult(Z, Z)))
% 11.12/2.74 = { by axiom 2 (c02) }
% 11.12/2.74 mult(mult(mult(mult(X, Z), mult(Y, Z)), mult(mult(X, Y), mult(Z, Z))), mult(mult(X, Y), mult(Z, Z)))
% 11.12/2.74 = { by axiom 4 (c04) }
% 11.12/2.74 mult(mult(X, Z), mult(Y, Z))
% 11.12/2.74 = { by axiom 2 (c02) R->L }
% 11.12/2.74 mult(mult(X, Y), Z)
% 11.12/2.74
% 11.12/2.74 Goal 1 (goals): mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))) = mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d))).
% 11.12/2.74 Proof:
% 11.12/2.74 mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))
% 11.12/2.74 = { by axiom 4 (c04) R->L }
% 11.12/2.74 mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d)))
% 11.12/2.74 = { by axiom 2 (c02) }
% 11.12/2.74 mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, c), mult(b, d))))
% 11.12/2.74 = { by axiom 4 (c04) }
% 11.12/2.74 mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, c), mult(b, d))))
% 11.12/2.74 = { by axiom 1 (c01) }
% 11.12/2.75 mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))))
% 11.12/2.75 = { by axiom 2 (c02) }
% 11.12/2.75 mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))), mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))))
% 11.12/2.75 = { by axiom 3 (c03) }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))))
% 11.12/2.75 = { by axiom 3 (c03) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))))
% 11.12/2.75 = { by axiom 1 (c01) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d)))))
% 11.12/2.75 = { by axiom 4 (c04) }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))))
% 11.12/2.75 = { by lemma 6 R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))))
% 11.12/2.75 = { by axiom 1 (c01) }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(a, b), mult(c, d)), mult(c, d))))
% 11.12/2.75 = { by lemma 6 R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(c, d))))
% 11.12/2.75 = { by axiom 4 (c04) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))))
% 11.12/2.75 = { by axiom 2 (c02) }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d)))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))))
% 11.12/2.75 = { by axiom 2 (c02) }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d)))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))))
% 11.12/2.75 = { by axiom 1 (c01) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(mult(c, d), mult(c, d)))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))))
% 11.12/2.75 = { by axiom 1 (c01) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(mult(c, d), mult(c, d)))), mult(mult(a, b), mult(mult(c, d), mult(c, d))))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))))
% 11.12/2.75 = { by lemma 7 }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(c, d))), mult(mult(a, b), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))))
% 11.12/2.75 = { by lemma 6 }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(a, b), mult(c, d)), mult(c, d))), mult(mult(a, b), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))))
% 11.12/2.75 = { by lemma 6 }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(a, b), mult(c, d)), mult(c, d))), mult(mult(a, b), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))), mult(mult(mult(a, b), mult(a, b)), mult(c, d)))))
% 11.12/2.75 = { by lemma 6 }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(a, b), mult(c, d)), mult(c, d))), mult(mult(a, b), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))), mult(mult(a, b), mult(c, d)))))
% 11.12/2.75 = { by axiom 2 (c02) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(a, b))), mult(mult(mult(a, b), mult(c, d)), mult(c, d))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d))))
% 11.12/2.75 = { by axiom 1 (c01) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(a, b)), mult(c, d))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d))))
% 11.12/2.75 = { by axiom 1 (c01) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d))))
% 11.12/2.75 = { by lemma 6 }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d))))
% 11.12/2.75 = { by axiom 1 (c01) }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d))))
% 11.12/2.75 = { by lemma 5 }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d)))))
% 11.12/2.75 = { by axiom 1 (c01) R->L }
% 11.12/2.75 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d)))))
% 11.12/2.76 = { by lemma 5 R->L }
% 11.12/2.76 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))), mult(mult(a, b), mult(c, d))))
% 11.12/2.76 = { by axiom 4 (c04) R->L }
% 11.12/2.76 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d)))), mult(mult(a, b), mult(c, d))))
% 11.12/2.76 = { by axiom 4 (c04) R->L }
% 11.12/2.76 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d)))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d)))))
% 11.12/2.76 = { by axiom 2 (c02) }
% 11.12/2.76 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, c), mult(b, d))))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d)))))
% 11.12/2.76 = { by axiom 2 (c02) }
% 11.12/2.76 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, c), mult(b, d))))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, c), mult(b, d))))))
% 11.12/2.76 = { by axiom 4 (c04) R->L }
% 11.12/2.76 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, c), mult(b, d))))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, c), mult(b, d))))))
% 11.12/2.76 = { by lemma 7 }
% 11.12/2.76 mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d))))
% 11.12/2.76 = { by axiom 4 (c04) }
% 11.12/2.76 mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))
% 11.12/2.76 % SZS output end Proof
% 11.12/2.76
% 11.12/2.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------